Preheat your oven to 375°F (190°C).
Heat the olive oil in a skillet over medium heat. Add the diced bell peppers, onions, and corn kernels. Sauté for about 5 minutes, or until the vegetables are softened and fragrant.
In a large mixing bowl, combine the cooked rotini pasta and shredded chicken. Add the sautéed vegetables, barbecue sauce, garlic powder, onion powder, smoked paprika, salt, and pepper. Stir until well combined and pasta is evenly coated.
Reserve about 1/2 cup of each cheese for topping. Fold the remaining cheddar and mozzarella into the pasta mixture.
Transfer the pasta mixture to a greased 9x13-inch baking dish. Sprinkle the reserved cheddar and mozzarella evenly over the top.
Bake in the preheated oven for 20-25 minutes until the cheese is melted, bubbly, and slightly browned. Let rest for 5 minutes before serving.