To make cookies: Cream butter, margarine and white sugar. Alternate dry ingredients (flour, baking powder, salt) and liquids (milk, almond extract). Fold in stiffly beaten egg whites and sliced almonds. Drop on a greased cookie sheet using cookie dough scoop. Bake in a preheated oven at 325° for 12 to 15 minutes (lightly browned on bottom only).
To make frosting: Cream powdered sugar and butter. Add milk (start with 1 tablespoon and add until smooth, creamy and spreadable) and almond extract. Frost when cookies are cool. Store layered between waxed paper. Garnish tops with additional sliced almonds.