Combine soy sauce, oil, Worcestershire, lemon juice, garlic, brown sugar, and pepper in a large bowl or resealable bag.
Add steak; toss to coat well. Refrigerate at least 2 hours or up to 8 hours for maximum flavor.
Preheat grill to medium-high. Soak wooden skewers in water 30 minutes beforehand, if using.
Thread marinated steak onto skewers, alternating with peppers, onion, and mushrooms.
Grill 10-12 minutes, turning every 3 minutes, until steak reaches desired doneness and vegetables are tender and slightly charred.
Remove; rest 3 minutes. Serve hot with preferred dipping sauce or over rice.