In a bowl, combine flours, sugar, baking powder, cream of tartar and salt. Cut in shortening until mixture resembles coarse crumbs. Beat egg and milk; stir into dry ingredients until a ball forms.
Turn onto a floured surface, knead 5-6 times. Roll to 1/2-in. thickness; brush with butter. Cut with a 2-in. biscuit cutter. Place on an ungreased baking sheet. Bake at 450° for 10-12 minutes or until golden brown.