Heat olive oil in a large pot over medium heat. Sauté garlic for 1 minute, then add onions and bell peppers. Cook until soft and translucent, about 10 minutes.
Stir in chili powder, cumin, paprika, salt, and pepper. Cook 1 minute. Pour in beer and scrape up any browned bits from the bottom of the pot. Simmer 10 minutes to reduce slightly.
Add pulled pork, tomato sauce, crushed tomatoes, and drained beans. Stir well to combine.
Turn heat to low and simmer for at least 1 hour until sauce thickens and flavors fully meld. Serve hot with your favorite toppings.