Preheat oven to 400 degrees F.
Whisk together the oil, chopped cilantro, chili powder, cumin, salt, garlic, pepper, and cayenne in a bowl; add the chicken and toss to coat.
Transfer chicken to a foil-lined baking sheet and arrange the green pepper, onion, and tomato over each. Roast until the largest piece is just cooked through, and an instant-read thermometer inserted in the thickest part reads 165 degrees F, about 20 minutes.
Remove the chicken from oven and immediately top with the cheese and serve as the cheese melts. Transfer the chicken to a platter or among plates and garnish with fresh cilantro leaves.