Preheat oven to 425°. Grease a baking sheet with shortening and set aside.
Sift flour, sugar, baking powder and salt into a bowl.
Blend butter into flour mixture with a pastry cutter or two knives until mixture resembles coarse corn meal.
Blend first egg with milk. Add to flour/fat mixture, stirring just until no flour shows. If necessary, add more milk so mixture forms a soft dough.
Sprinkle additional flour over mixture and roll onto a floured surface. Knead 15 times, then shape into a ball. Divide into half. Flatten to 1/2" thickness. With floured knife, cut ball into 8 pie-like wedges.
Place wedges on a prepared baking sheet one inch apart. Brush with beaten egg.
Bake 10-12 minutes until deep golden brown. Serve immediately. Two per serving.