Heat the olive oil in a large pot over medium heat. Add the onion and green bell pepper. Cook for 5 minutes until the vegetables soften.
Stir in the garlic and cook for 1 minute until fragrant.
Add the black beans, diced tomatoes, chili powder, cumin, vegetable broth, salt, and pepper. Stir everything together and bring the mixture to a simmer.
Reduce the heat to low and let the chili cook uncovered for 20 minutes, stirring occasionally until it thickens.
While the chili simmers, preheat the oven to 400 degrees and grease a baking pan.
In a mixing bowl, combine the cornmeal, flour, baking powder, and sugar. In a separate bowl, whisk together the milk, egg, and vegetable oil.
Pour the wet ingredients into the dry ingredients and stir until just combined. Spread the batter evenly in the prepared pan.
Bake the cornbread for 20 minutes until the top turns golden and a toothpick inserted in the center comes out clean.
Let the cornbread cool for a few minutes, then cut it into squares and serve alongside the chili.