Heat the olive oil in a large oven-safe pot over medium heat. Add the onion, garlic, and bell pepper. Cook for 5 minutes until the vegetables soften.
Stir in the chili powder, cumin, cayenne, and salt. Cook for 1 minute until the spices smell fragrant.
Add the black beans, kidney beans, pinto beans, and diced tomatoes. Bring the mixture to a gentle simmer and cook for 10 minutes, stirring now and then.
While the chili simmers, mix the cornmeal, flour, sugar, and baking powder in a bowl. In a separate bowl, whisk the milk, egg, and melted butter together. Combine the wet and dry ingredients until just mixed.
Drop spoonfuls of the cornbread batter over the simmering chili. Use the back of a spoon to spread it into an even layer.
Transfer the pot to a 400°F oven and bake for 20 minutes until the cornbread is golden and a toothpick inserted in the center comes out clean.