Brown beef in a large Dutch oven over medium-high about 10 minutes until no pink remains, breaking up with a spoon. Drain fat, leaving about 2 tablespoons.
Cook onion and pepper about 6 minutes until soft; add garlic and cook 1 minute until fragrant.
Stir in chili powder, cumin, paprika, and cayenne; cook 1 minute to bloom spices.
Add beer; scrape up browned bits with a wooden spoon. Simmer 5 minutes to reduce slightly.
Stir in beans, tomatoes, paste, broth, sugar, salt, and pepper.
Boil; reduce heat to low and simmer partially covered 2 hours, stirring every 20 minutes.
Uncover; simmer 15 more minutes to desired thickness.
Adjust seasoning; serve with cornbread, cheddar, and diced onions.