If serving with rice, start cooking it now. Rinse both cans of beans under cold water in a colander for about 30 seconds. Mince the garlic.
Heat oil in a skillet over medium heat until shimmering. Add minced garlic and cook for about 1 minute, stirring constantly, until fragrant and golden. Don't let it burn.
Add ground beef to the skillet. Break it up with a spatula and cook for 5-7 minutes until no pink remains. If using fattier beef, drain excess grease.
Add the rinsed kidney beans and black beans to the beef. Stir gently to combine and let warm for about 1 minute.
Add tomato sauce, tomato paste, apple cider vinegar, brown sugar, molasses, Dijon mustard, and Worcestershire sauce. Then add smoked paprika, garlic powder, onion powder, cayenne pepper, and black pepper. Stir everything together well.
Bring mixture to a gentle simmer. Reduce heat to medium-low and simmer for 5 minutes, stirring every minute or so, until sauce thickens and flavors meld together.
Taste and add salt as needed (start with 1/2 tsp). Adjust seasoning if needed - add more vinegar if too sweet, or sugar if too tangy.
Serve about 1 cup of BBQ beef and beans over 1 cup of rice per person. Top each serving with 1/4 cup shredded cheddar cheese and sliced green onions.