Bring water and chicken stock to a simmer in a heavy bottomed pot. Remove the pot from heat, add the dried mushrooms, cover and allow to steep until the mushrooms have softened (about 15 minutes). Remove the mushrooms with a slotted spoon and set aside. Strain the stock through a fine mesh cheesecloth or coffee filter to remove the grit and set aside.
In the same pot, bring the oil and butter to a shimmer over medium-high heat. Add onions and shallots and stir until they’re just beginning to color. Add garlic, stir for one minute, then add the celery, fresh mushrooms, reconstituted mushrooms and salt. Continue to stir the mushrooms until they release their water and begin to color. Deglaze with the cognac and madeira and cook off for 30 seconds. Add the chicken stock and thyme or marjoram, then simmer for 30-35 minutes. Remove from the heat and, when cool enough, puree the soup in batches using a blender, then pass through a medium strainer.
To serve, stir in crème fraîche and truffle jus. Melt cheese over toasted crostini. In a bowl, pile the sautéed mushrooms into the middle, then pour the bisque around the pile. Garnish with rosemary flowers or a sprig of fresh thyme, a drizzle of porcini or truffe oil and the cheese crostini.
If you are preparing the bisque in advance, chill the soup after pureeing and straining.