Place beef in a shallow dish; pour 2 tablespoons soy sauce over beef. Turn to coat completely. Let marinate 15 minutes in refrigerator.
Combine orange juice, sugar, 2 tablespoons soy sauce, vinegar, orange rind, and red pepper in a small bowl. Stir with a whisk.
Heat oil in a large nonstick skillet over high heat. Add beef, and cook 6 minutes. Remove from heat, and place on a serving platter; keep warm.
Reduce heat to medium-high; add carrot and onion. Cook 7 minutes or until carrot is lightly browned and crisp-tender, stirring frequently. Increase heat to high; add beef and its juices, and orange juice mixture. Cook 3 minutes or until slightly thickened.