Preheat oven to 375 degrees F. Lightly grease a 9x13 inch baking dish.
Season chicken: toss diced chicken with olive oil and all spices until evenly coated.
Layer: spread rice in the bottom of the dish. Add peppers, onion, and black beans if using.
Add liquid: pour chicken broth and salsa over the dish. Stir gently to combine liquids.
Add chicken: arrange seasoned chicken on top in a single layer.
Bake covered: cover tightly with foil. Bake 40 minutes.
Stir and add cheese: remove foil, stir gently. Scatter cheese on top. Bake uncovered 10 to 15 more minutes until cheese melts and chicken reaches 165 degrees F.
Rest and serve: rest 5 minutes. Top with cilantro, sour cream, and lime if desired.