For filling, cook ground beef in a small skillet until brown. Drain off fat. Stir in taco sauce, chili powder, onion powder, and garlic powder. Set aside.
Unroll pizza dough. Roll dough into a 14x10-1/2-inch rectangle. Cut into twelve 3-1/2-inch squares. Divide filling among dough squares. Sprinkle with cheese. Brush edges with water. Lift one corner of each square and stretch dough to the opposite corner, making a triangle. Press edges well with a fork to seal.
Arrange on a greased or parchment-lined baking sheet. Prick with fork. Combine egg and the 1 teaspoon water; brush onto turnovers. Bake in a 425 degree F oven for 8 to 10 minutes or until golden. Let stand 5 minutes before serving.