Cut steak diagonally across the grain into thin slices. Combine steak, cornstarch, salt, and white pepper in a bowl, tossing to coat; set aside.
Heat 2 teaspoons oil in a large nonstick skillet over medium heat. Add steak to pan; stir-fry 4 minutes or until browned. Remove steak from pan. Add remaining 1 teaspoon oil to pan. Add bell pepper, carrot, and ginger; stir-fry 2 minutes or until carrot is tender. Add broth and chile paste; cook 3 minutes. Return the steak to pan; cook 1 minute or until thoroughly heated. Serve over rice.