Heat the oil in a large pot over medium-high heat. Add the onions, bell peppers, and garlic and cook, stirring occasionally, until soft, 6 to 8 minutes.
Add the beef and cook, breaking it up with a spoon, until no longer pink, 5 to 7 minutes. Add the tomato paste, chili powder, and cumin and cook, stirring, for 2 minutes.
Add the beer, beans, the tomatoes and their juices, 2 1/2 teaspoons salt, and 1/2 teaspoon pepper. Simmer over medium heat, stirring occasionally, until thickened, 20 to 25 minutes. Serve with the corn bread and toppings as desired.