Combine 2 cups flour, baking powder, and salt; stir well. Cut in butter until mixture resembles coarse meal. Sprinkle milk evenly over flour mixture, stirring just until dry ingredients are moistened.
Beat egg whites (at room temperature) until stiff peaks form; fold into flour mixture. Sprinkle remaining flour evenly over kneading surface. Turn dough out onto a floured surface; knead lightly 10 to 12 times.
Roll dough to 1/2-inch thickness; cut with a 2-inch biscuit cutter. Place biscuits on a greased baking sheet. Bake at 450° for 12 minutes or until lightly browned.