Preheat oven to 375°. Butter a shallow 1 1/2-quart casserole. Melt 1 Tbsp. butter in a medium skillet over medium-high heat. Add mushrooms and cook for about 6 minutes. Remove from heat. Beat eggs, milk, salt and pepper in a bowl. Stir in mushrooms, potatoes and cheese. Place in casserole and bake for 35 to 45 minutes.