Clean the mushrooms of any dirt & debris (rinsing briefly under cold running water if necessary). Cut into strips 1/4 inch thick.
Peel the carrots and onions and dice into 1/4 inch squares. Trim the celery and cut into 1/4 inch squares. Slice the fingerlings into 1/4 inch thick rounds.
Melt the butter in a large pot over medium heat. Add the celery, carrots & onion and cook, stirring occasionally, until slightly softened, about 6 minutes. Add the diced matsutake mushrooms, stir well and cover the pot. Cook for another 5 – 10 minutes, or until the mushrooms have softened and released their liquid. Add the bay leaf, a twist or two of pepper from the pepper grinder and a good pinch of salt. Add the chicken stock and sliced fingerling potatoes, stir and cover the pot. Reduce the heat to low and simmer for 15 – 20 minutes or until the potatoes yield when pierced with a fork.
Whisk the flour into the milk until all the flour is completely incorporated and the mixture is smooth and free of lumps. Stir into the soup and simmer for another 10 minutes or until the soup has thickened slightly. If the soup is too thick, add more milk until the desired texture is achieved. Adjust salt & pepper to taste.
Note: for added richness, substitute 1/2 cup of heavy cream for 1/2 cup of the milk.
This soup reheats well. Like many soups, the flavor will improve over the next day or two.