Heat broiler with rack set near top of oven. Heat oil in a large frying pan over high heat. Add steak to pan and cook, stirring occasionally, until starting to brown, about 3 minutes. Transfer steak to a plate. Add bell peppers, onion, salt, and pepper to hot pan and cook until vegetables have softened, about 8 minutes. Return meat to pan and cook until mixture is hot.
Spread each roll with 1 tsp. mustard. Put a slice of cheese in each opened roll, set on a baking sheet, and broil to toast roll and melt cheese, about 2 minutes. Top with warm steak mixture.