Cook rice according to package directions; keep warm.
Heat 1/2 teaspoon oil in a large nonstick skillet over medium-high heat. Add onions and ham; stir-fry 1 minute. Add bean sprouts, and stir-fry 30 seconds. Remove from heat.
Combine the eggs, egg whites, stir-fry sauce, and white pepper, and beat well. Stir in ham mixture. Heat 1/2 teaspoon oil in pan over medium-high heat, and pour half of egg mixture into pan. Cook 45 seconds on each side or until the egg mixture is lightly browned. Remove from pan, and keep warm. Repeat with 1/2 teaspoon oil and egg mixture. Serve over rice.