Preheat your oven to 400°F / 200°C. Lightly grease a 3-quart rectangular baking dish (or a 9x13 inch pan) and set it aside.
In a large skillet, heat the vegetable oil over medium heat.
Add the chopped sweet pepper and onion, cooking and stirring occasionally until they soften, about 5-7 minutes.
Add the minced garlic and cook for one more minute until fragrant.
Stir in the slightly mashed kidney, pinto, and black beans.
Pour in the vegetable juice, undrained green chiles, chili powder, and cumin.
Stir everything together and bring the mixture to a gentle simmer, allowing it to heat through.
Carefully transfer the hot bean mixture into your prepared baking dish and spread it into an even layer.
In a separate bowl, prepare the corn muffin mix according to the package directions. Gently fold in the shredded cheddar cheese and snipped cilantro until just combined—be careful not to overmix.
Spoon the cornbread batter evenly over the bean mixture in the baking dish, spreading it to cover the surface.
Bake, uncovered, for 20 to 25 minutes, or until the cornbread topping is golden brown and a toothpick inserted into the center of the cornbread comes out clean.
Let the casserole cool for a few minutes before serving.
Top with salsa and sour cream, if desired.