Preheat oven to 375 degrees F. Line a large rimmed baking sheet with parchment paper.
Place sliced bell peppers, onions, mushrooms, and garlic on parchment paper and drizzle with olive oil and Worcestershire and sprinkle with salt and pepper; toss well to coat. Roast on the middle rack for 12-14 minutes or until tender. Broil 1-2 minutes or until onions just begin to turn golden at the edges. Remove from oven.
Add beef; toss. Broil 2 minutes more. Top with cheese. Broil for 1-2 minutes or until cheese is melted. Serve hot.