Preheat and prep: Heat the oven to 375°F (190°C). Lightly coat a 9x13-inch baking dish with nonstick spray.
Cook the chicken (if not using rotisserie): Season chicken breasts with salt, pepper, and a pinch of smoked paprika.
Sear in 1 tablespoon olive oil over medium heat for 3–4 minutes per side, then cover and cook until done, or bake at 375°F until the internal temp hits 165°F. Let cool slightly, then shred or dice.
Mix the sauce base: In a large bowl, whisk together BBQ sauce, Greek yogurt, egg whites (if using), smoked paprika, chili powder, garlic powder, onion powder, 1/2 teaspoon salt, and black pepper. The mixture should be creamy and pourable.
Add the fillings: Fold in shredded chicken, black beans, corn, bell peppers, red onion, and cooked brown rice or cauliflower rice.
Stir until everything is evenly coated. Taste and adjust seasoning.
Layer and top: Spread the mixture into the baking dish, smoothing it into an even layer. Sprinkle cheese evenly over the top.
Bake: Bake uncovered for 22–28 minutes, or until the casserole is bubbling at the edges and the cheese is melted and lightly golden.
Rest and garnish: Let the casserole rest for 5–10 minutes to set.
Top with chopped cilantro or green onions if you like. Slice and serve warm.