Preheat your oven to 400°F (200°C). Lightly oil a large oven-safe skillet (about 12 inches, cast iron works well) or a 9×13-inch baking dish.
In a large bowl, combine the sliced chicken, 2 tablespoons of olive oil, lime juice, minced garlic, cumin, chili powder, smoked paprika, dried oregano, salt, black pepper, and cayenne (if using). Toss well until all the chicken is evenly coated. Let it sit while you prep the vegetables so it can marinate briefly.
2 pounds boneless, skinless chicken breasts, 3 tablespoons olive oil, 4 tablespoons lime juice, 3 cloves garlic, 2 teaspoons ground cumin, 2 teaspoons chili powder, 1 teaspoon smoked paprika, 1 teaspoon dried oregano, 1–1½ teaspoons kosher salt, 1/2 teaspoon black pepper, 1/4–1/2 teaspoon cayenne pepper
Add the sliced bell peppers and onion to the same bowl with the seasoned chicken. Toss until the vegetables are well coated with the spices and oil. If the mixture looks dry, add the remaining 1 tablespoon of olive oil.
3 bell peppers, 1 large yellow onion, 3 tablespoons olive oil
Spread the chicken and vegetable mixture evenly in the prepared skillet or baking dish. Try to keep everything in a single layer so it roasts rather than steams.
Bake for 20–25 minutes, stirring halfway through, until the chicken is cooked through (165°F on an instant-read thermometer) and the peppers and onions are tender with some browned edges. If needed, bake an additional 5 minutes.
Remove the skillet from the oven and sprinkle the shredded cheese evenly over the hot chicken and vegetables. Return to the oven for 5–7 minutes, or until the cheese is melted and bubbly. For browned spots, switch the oven to broil for the last 1–2 minutes, watching closely.
1 1/2 cups shredded cheese
Let the skillet rest for about 5 minutes so the juices settle. Sprinkle with chopped cilantro. Serve straight from the skillet with warm tortillas, lime wedges, and your choice of toppings such as avocado or guacamole, salsa or pico de gallo, sour cream or Greek yogurt, pickled jalapeños, cotija cheese, and radish slices.
1/2 cup fresh cilantro, 8–12 small flour or corn tortillas, sliced avocado or guacamole, salsa or pico de gallo, sour cream or plain Greek yogurt, pickled jalapeños, crumbled cotija cheese, fresh radish slices and lime wedges