Preheat the oven to 375°F and lightly grease an 8x8 baking dish.
Heat the olive oil in a large skillet over medium heat. Add the onion, garlic, and bell pepper. Cook for 5 minutes until the vegetables soften.
Stir in the cumin and chili powder, then add the rice. Cook for 1 minute to toast the rice lightly.
Pour in the black beans, diced tomatoes with green chilies, and vegetable broth. Season with salt and black pepper. Bring the mixture to a simmer and cook for 5 minutes, stirring once.
Transfer everything to the prepared baking dish. Cover with foil and bake for 25 minutes.
Remove the foil, sprinkle the shredded cheese evenly over the top, and bake uncovered for 10 more minutes until the cheese melts and the rice is tender.