Cook onions in butter until tender in 10-inch skillet over medium-high heat. Beat eggs with milk, salt, and pepper sauce. Stir in rice, tomato, and chilies. Pour into skillet. Reduce heat to medium-low. Cover; cook until top is almost set, 12 to 15 minutes. Sprinkle with cheese. Cover, remove from heat, and let stand about 10 minutes. Conventional Oven: Combine eggs, milk, salt, and pepper sauce in large bowl; whisk to blend. Stir in rice, tomato, cheese, chilies, and onions. Pour into greased 10-inch baking dish. Bake at 375 degrees 30 minutes or until knife inserted in center comes out clean.