In a large pan over medium-high heat, warm oil. Add the onion and cook about 10-12 minutes, until lightly browned. Add the garlic and beef, cooking about 5 minutes, until meat is no longer pink. Add chili powder, cayenne, cumin, salt, pepper, and tomato paste, stirring to combine, cooking for 3-5 minutes.
Serve in tortillas or taco shells and top with desired toppings.