Preheat your oven to 375°F (190°C) to prepare for baking.
Carefully slice the tops off the bell peppers and scoop out the seeds and membranes. Stand the peppers upright in a large baking dish, ensuring they are stable.
In a spacious skillet over medium heat, pour in the olive oil. Once hot, add the cubed chicken breast. Season with salt, pepper, chili powder, cumin, and smoked paprika. Sauté for about 5-7 minutes, stirring occasionally, until the chicken is browned and fully cooked.
Introduce the sliced onion and both varieties of bell pepper into the skillet, continuing to sauté for an additional 5 minutes until the vegetables are softened and aromatic. Add the minced garlic and stir for another minute, allowing the garlic to become fragrant.
Mix in the corn and black beans into the chicken and vegetable mixture. Stir well to ensure everything is uniformly combined and heated through.
Remove the skillet from the heat. Using a spoon, generously fill each prepared bell pepper with the chicken mixture, packing it in tightly. Top each stuffed pepper with a generous layer of shredded cheddar cheese.
Cover the baking dish with aluminum foil and place it in the oven. Bake for 25 minutes. After this time, carefully remove the foil to allow the cheese to brown, and bake for an additional 10 minutes, or until the cheese is melted, bubbly, and has a delightful golden color.
Once baked, take out the stuffed peppers and let them cool for a few minutes. Garnish with fresh cilantro. Serve immediately with lime wedges on the side to squeeze over the top, adding a burst of zesty freshness.