Combine flour, baking powder, and salt; stir well. Cut in shortening until mixture resembles coarse meal. Stir in cooled potatoes. Sprinkle milk over flour mixture; stir until dry ingredients are moistened.
Turn dough out onto a lightly floured surface, and knead 10 to 12 times.
Roll dough to 1/2-inch thickness; cut with a 1 3/4-inch biscuit cutter. Place biscuits on a greased baking sheet. Bake at 450° for 8 minutes or until lightly browned.