Heat oven to 350°F. Bake biscuits as directed on bag. Cool slightly, about 5 mintues.
Meanwhile, beat egg and milk in small bowl with fork until well mixed. In 7 or 8-inch nonstick skillet, heat butter over medium heat until melted. Add egg mixture; cook, stirring occasionally, until eggs are desired doneness and still moist.
Split biscuits horizontally. Layer cooked eggs, bacon and cheese on bottom halves of biscuits; top with biscuit tops.