Heat 1 tablespoon oil in a large Dutch oven over medium-high; brown beef about 6-8 minutes, breaking up with a spoon. Transfer to a bowl.
Add remaining oil; brown pork about 6-8 minutes until cooked through. Transfer to beef bowl.
Cook onion in same pot about 5 minutes until soft; add garlic and cook 1 minute until fragrant.
Stir in chili powder, cumin, paprika, oregano, and cayenne; cook 30 seconds until fragrant.
Return meats; stir in tomatoes, paste, and broth.
Boil; reduce heat to low and simmer uncovered 1.5 hours, stirring occasionally.
Add all three beans, salt, pepper, and sugar; simmer 30 more minutes.
Adjust seasoning; serve hot with preferred toppings, such as cheese, sour cream, and green onions.