Preheat oven to 325°. In a large frying pan over high heat, melt 2 tablespoons butter. Add mushrooms and cook, stirring often, until lightly browned, about 5 minutes.
Butter an 8-inch square baking dish and sprinkle cheese on the bottom. In a small bowl, mix cream, mustard, thyme, salt, and pepper. Pour half the cream mixture over the cheese. Top with mushrooms and eggs. Pour remaining cream mixture over the top. Bake until eggs are set, about 35 minutes.
Note: Nutritional analysis is per serving.