Heat oven to 325 degrees with the rack positioned at the top. Butter a deep 8-inch round, square or oval casserole generously and sprinkle all over with bread crumbs.
Heat the 2 tablespoons butter in a large pan over medium-high heat. When melted and foamy, add the mushrooms and cook until lightly browned, about 3 to 5 minutes. Scatter the cooked mushrooms and grated cheese over the bread crumbs.
Whisk together the half-and-half, whole milk, eggs, salt, pepper and nutmeg. Pour the mixture over the cheese. Sprinkle the top with Parmesan, and bake until the top is golden and the custard is just set in the center, about 40 to 45 minutes. Set aside 5 to 10 minutes to cool before serving.