In a large resealable plastic bag, combine 3 tablespoons soy sauce and pepper; add beef. Seal bag and turn to coat; refrigerate for 30-60 minutes. In a small bowl, combine the broth and remaining soy sauce until smooth; set aside.

Drain and discard marinade from beef. In a large nonstick skillet or wok, stir-fry the garlic and ginger in 2 teaspoons oil for 1 minute.

Stir-fry the peppers in remaining oil for 1 minute. Add mushrooms; stir-fry 2 minutes longer or until peppers are crisp-tender. Stir broth mixture and add to vegetable mixture. Bring to a boil; cook and stir for 2 minutes or until thickened.

Meanwhile, heat grill and cook steaks until desired doneness is achieved.

Serve vegetable mixture over steak and serve with rice if desired.