heat the olive oil over medium-high in a large skillet or stockpot. Add the onions, garlic, carrot, celery, and peppers; season with salt and pepper to taste. Cook until the vegetables become soft, about 10 minutes.

Add the ground beef to the skillet and break it up with a fork. Cook until the beef begins to brown, about 5 minutes. Stir in the chili powder and cumin; cook until fragrant, about 1 minute. Add the tomatoes and bring the chili to a boil. Reduce the heat and simmer until thickened about 15 minutes. Stir in the beans and lime juice.

While the chili is cooking, preheat the oven to 375˚F. In a medium-sized bowl, whisk together cornmeal, flour, salt, baking powder, and sugar until combined. Make a well in the center and add the egg, melted butter, Greek yogurt, and oil; stir with a fork before incorporating into the dry ingredients. Fold in the cheese and set aside.

Baking the Casserole: Once the chili has thickened, add it to a deep 9 by 13-inch baking pan. Using a scoop or spoon, drop dollops of cornbread batter on top of the chili. Bake for 25 to 30 minutes, or until the cornbread is golden and the chili is bubbling. Garnish with scallions, fresh cilantro, cherry tomatoes, additional cheese, and sour cream if desired.