Heat the olive oil in a large pot over medium heat. Add the onion and red bell pepper and cook for 5 minutes until they soften.
Stir in the garlic, chili powder, and cumin and cook for 1 minute until fragrant.
Add the black beans, kidney beans, diced tomatoes, frozen corn, and vegetable broth. Bring the mixture to a simmer and cook for 20 minutes, stirring occasionally.
While the chili simmers, preheat the oven to 400°F and line a 12-cup muffin tin with paper liners.
In a mixing bowl, whisk together the cornmeal, flour, baking powder, and sugar. In a separate bowl, whisk the milk, egg, and melted butter. Pour the wet ingredients into the dry and stir just until combined.
Divide the batter among the muffin cups and bake for 15 minutes until the tops are golden and a toothpick comes out clean.
Ladle the chili into bowls, top with shredded cheddar cheese and sliced avocado, and serve with the warm cornbread muffins on the side.