Place the dried mushrooms and stock in a pot. Bring to a low simmer and heat to reconstitute.
Heat the oil in a soup pot over medium-high heat. When it begins to ripple, add the fresh mushrooms and cook until lightly browned and tender, 12 to 15 minutes. Add the thyme, garlic, shallots and bay leaf, and then season with salt and pepper. Stir to soften, 2 to 3 minutes. Deglaze the pan with marsala and cook to reduce by half.
Remove the plump, reconstituted dried mushrooms from their stock and chop. Then add the mushrooms and the mushroom stock to soup pot, discarding the last few spoonfuls of stock where grit may have settled. Add 2 cups water to the soup, and simmer a few minutes. Taste and adjust the seasoning. Cool to store for a make-ahead meal.
Reheat over medium heat. To serve, add the parsley and stir in the lemon juice to the soup. Place a small round of fried toast in each soup bowl, sprinkle with a little cheese and top with the soup.
The fresh mushrooms for this dish can be a mix of crimini, shiitake, white button, wood ear or whatever varieties look best and have a fair price per pound.