Beat eggs, milk, salt and pepper until uniform in color. Melt butter in skillet over medium heat. Pour egg mixture into skillet. Cook, stirring occasionally until thickened, about 3 to 5 minutes. Set aside.
Roll biscuits 1/8-inch thick, keeping them circular. Divide egg mixture evenly between biscuits, placing it on one side of the biscuit. Place the cheese on top of the egg mixture. Fold over other half of biscuit and seal halves together.
Place on a greased cookie sheet and bake at 350 degrees for 10 to 15 minutes or until golden brown.