This savory dish of gratineed mussels on the half shell is based on a classic French recipe.
Bring wine to a simmer in a large skillet over high heat. Add mussels, and cook, stirring frequently, until the mussels have opened, up to about 5 minutes. Transfer mussels as they open to a bowl to cool. Strain cooking liquid through a fine mesh strainer into a measuring cup, reserving 1 cup liquid and discarding any grit.
Discard any mussels that did not open or that have broken shells. Open each mussel, discarding the empty half shell. Loosen each mussel from shell, and arrange mussels on an oven-proof platter or rimmed baking sheet. Cover with plastic wrap; refrigerate while making sauce.
Mash 1 tablespoon butter with flour until smooth; set aside. Melt remaining tablespoon butter in a small saucepan over medium heat. Add mushrooms, and cook until tender, about 4 minutes. Add reserved mussel liquid, and bring to a boil. Whisk in the butter-and-flour mixture. Whisk in the cream, lemon juice, salt, and pepper. Simmer until reduced by two-thirds and thickened. Remove pan from heat, and keep warm.
Heat broiler. Position rack 3 to 4 inches from heat. Remove mussels from refrigerator, and spoon sauce over each one until well coated. Sprinkle with grated cheese, and place under broiler until golden brown, 3 to 4 minutes. Serve immediately.