This is, what people might call a classical gap filler. Having never been convinced with Éowyn's more than sudden turn to gardening and healing, I never could quell the suspicion that the Professor somehow forgot to tell us some important aspect of the growing relation between Éowyn and Faramir. Well, and this is my quess at what might have happened.
Texts in italics at the beginning and the end of the story are quotes from "The Return of the King"
Ranunculus Glacialis is Latin for "glacier crowfoot", one of the flowers I love most, as you may well understand, reading the text.
And tidings now came by swift riders from Cairn Andros of all that was done, and the City made ready for the coming of the King.(...); but Faramir did not go, for now being healed he took up his authority and the Stewardship, although it was only for a little while, and his duty was to prepare for one who should replace him.
And Éowyn did not go, though her brother sent word, begging her to come to the field of Cormallen. And Faramir wondered at this...
He pushed his chair back and went over to the window, to look out into the soft grey of an overcast morning. Another sleepless night had passed and again dawn had found him at the desk in his study, drugging himself with work to keep the nightmares at bay.
Organizing life in a partly destroyed city, arranging the return of the evacuated women and children, managing supplies and accommodation for thousands of soldiers, not to mention the special care the many wounded requested, preparing for the coronation that would make his office redundant...No, he knew the last to be wrong, though at times he was not sure, if he thought it to be a boon or a curse to be the Steward of Gondor, taking up the position his father had held. He tried to push the upcoming uneasiness to the back of his mind. From the yard muffled noises could be heard: the change of the guards, a cart rumpling by, the White City slowly awaking and setting to her morning scores.
The King had sent word...Why had she not left for Cormallen? He leaned his forehead against the cool windowpane, closing his tired eyes. Was she still looking east?
..."But the healers would have me lie abed seven days yet...And my window doesn't look eastward."
He could still hear her words echo in his mind as he would never forget his first sight of her: slender but strong, wounded but fierce, sad but determined, maid and warrior in one, contradicting everything he had experienced up to that moment. Yet it had been pity, that had moved him so deeply, when he had first seen her. The pity he felt for the falcon with a broken wing, and his heart had ached to comfort her. Later understanding and admiration had grown...but when had his initial pity and admiration turned into love? When had he realized that he would never be whole again without her?
And as he stood there, absorbed in the softness of the morning, he suddenly realized, it had been well before they had stood on the walls together, the day of Sauron's downfall, when their hands had met and clasped.
It had been that day, sunny but still cool, rather promising spring than displaying it, that day, they had been walking in the garden of the Houses once again, in the fragrance of the herbs, when she had started to talk. How surprised he had been at her knowledge about each plant and its virtue. How delighted he had been, to discover this totally new trait in this stern, proud woman. He had been fascinated and they had talked at length about all kind of plants, the ranger of the South and the shieldmaiden of the North.
Stepping back from the window, he poured himself some well-watered wine and went to bend on his paperwork again but before his mind a scene recalled, pulling him in, making him stand beside her again in the pale spring sun and the sweet smell of the garden.
"Is there any plant you like best?" When her eyes had lit up at his question he had halfway expected her to name the ash, the water-loving tree of life, yet dealing death in the shape of the swift spears of the Rohirrim. But she had smiled, tilting her head , and his heart had skipped a beat, sensing something unexpected to come.
Taking a deep breath she had finally asked: "Do you know the flower called Glacier Crowfoot in the common tongue?"
"Why, surely any ranger should know it. A most lovely one, and as I know, no other flower ascents as high as that one in the mountains, even to places extremely threatened by frost. But surely its beauty deserves something better than being named after the carrion bird's feet. In Gondor it grows on the slopes of the White Mountains. But we prefer to call it Glacier Buttercup."
"Buttercup!" She had simply snorted with disgust. "Nay, Lord, don't give it a name that belittles its courage! Beautiful it may be, but it is not one to dally with, because it is poisonous, as you probably know. And don't despise the carrion birds for the work they do; it's the battles of Men that feed them." Her face had gone stern again, her eyes stony, looking away from him she had stood there, her shoulders squared, her fists clenched in the folds of her skirt.
His heart had sunk, feeling her tenseness and hurt. He had meant to be friendly, forgetting for one short moment, how thin the cover of comfort was, spread over fathomless despair. Like a sleeper, suddenly woken from soothing dreams by an icy gush of rain, he had realized what he had known in his heart all the time: slender and beautiful she might be, but whatever might come her way, she was of Eorl's root, a shieldmaiden, proud and strong, and well alert to strike with steel and word if she found it necessary to defend herself.
She had not turned to him but slowly started to speak again. "As you said, no flower blooms that high, no one endures frost and snow like it, and none can adapt to dire fate the way it does, even drawing in leaves and buds again that had already grown, to store the strength in its roots, that it may survive, biding its time to bloom again, when the frost is over."
And all of a sudden, he had seen her very soul before him, had understood her recklessness, her attitude towards fight and death, had understood, what had moved her, pushed her forward into battle, what had kept her alive yet through loneliness and despair, and he had felt a painful urge sweep through his entire being, the wish to be able to melt the frosts of the winter that held her imprisoned.
A little white flower amongst the bare black rocks, enduring year after year, roots clawed into the stone, waiting for its chance to bloom.
How he had wished to shelter her in the warmth of his embrace, to hold her, kiss her, and make her pale cheeks turn ruby with life, like the flowers petals, when bringing forth fruit. "Lady," forcing his breath to even he had stepped up to her. "I did not intend to belittle courage and endurance but wanted to praise beauty where it gladdens the eye."
Slowly she had turned to him, and he had felt himself drown in the pools of her eyes. She had blushed, but her look had never wavered, as she spoke in a low voice, little more than a whisper. "And yet there is another name for it in my country, one you might find more to your liking. Hvít Snáwbrýd the Rohirrim call it, White Snowlass in the common language, though it could be translated otherwise..." She had hesitated, her blush deepening and after a short moment had taken her leave from him quickly pacing back to the Houses.
He clasped the goblet. Had she realised that being a scholar he might know some Rohirric, might know the other meaning of that word? "Hvít Snáwbrýd," he murmured. Would she ever be that to him?... White Snowbride, overcoming frost and hardship?
A knock at the door of his study woke him from his reverie. "My Lord Steward." The Warden bowed somewhat awkwardly. "Excuse me for calling upon you that early, but as it is on one of my patients' behalf, I thought that you would not mind. You see, the Lady Éowyn..."
...and she dwelt in the Houses of Healing and walked alone in the garden, and her face grew pale again, and it seemed that in all the City she only was ailing and sorrowful. And the Warden of the Houses was troubled, and he spoke to Faramir.
Then Faramir came and sought her...