Preheat oven to 450°.
Heat a small nonstick skillet coated with cooking spray over medium-high heat. Add onion and sugar; sauté 8 minutes or until golden brown. Cool.
Lightly spoon flour into dry measuring cups; level with a knife. Place flour, baking powder, baking soda, and salt in a food processor; pulse 2 times or until blended. Add the shortening, and pulse 2 times or until combined. Sprinkle onion mixture over flour mixture. With processor on, slowly add buttermilk through food chute; process until dough forms a ball.
Turn dough out onto a floured surface, and knead lightly 4 to 5 times. Pat dough into an 8 x 6-inch rectangle; cut into 12 squares. Place on a baking sheet. Combine egg and water, and brush over biscuits. Bake at 450° for 11 minutes or until golden.