In a 10- to 12-inch frying pan over high heat, melt 2 tablespoons butter. Add mushrooms, onion, and nutmeg. Stir often until mushrooms are lightly browned, about 10 minutes. Season to taste with salt and pepper. Let cool.
Meanwhile, in a bowl, beat eggs to blend with crumbs, cilantro, and all but 1/2 cup of the cheese.
Coarsely chop the mushroom mixture and stir into the egg mixture. Pour into a buttered 8-inch square pan.
Bake in a 325° oven until center feels firm when lightly pressed, about 30 minutes (about 20 minutes in a convection oven). Sprinkle evenly with remaining cheese and bake just until it begins to melt, 3 to 4 minutes more (1 to 2 minutes in a convection oven). Remove from oven and let stand in pan until warm, at least 15 minutes, or until cool. Cut into 1-inch pieces and arrange on a platter.