Combine egg and egg white, beating well.
Heat 1 teaspoon sesame oil in a large nonstick skillet over medium-high heat. Add egg and egg white to skillet. As egg begins to cook, gently lift edges with a spatula, and tilt pan to allow uncooked portion to flow underneath. When set (about 30 seconds), turn egg over; remove from pan. Break into coarse pieces with spatula; set aside and keep warm.
Add remaining 2 teaspoons oil, garlic, and ginger to pan; stir-fry 1 minute. Add bell pepper; stir-fry 2 minutes. Add chicken and peas; stir-fry 1 minute. Add rice and teriyaki sauce; stir-fry 1 minute or until rice is thoroughly heated. Add cooked egg and green onions, stirring to combine. Serve immediately.