Brown the ground beef in a large skillet over medium heat, breaking it up as it cooks. Add the diced onion and minced garlic and cook until the onion softens.
Transfer the beef mixture to the slow cooker. Stir in the baked beans, barbecue sauce, smoked paprika, chili powder, salt, and black pepper until evenly combined.
Cover and cook on low for 6 hours or on high for 3 hours, stirring once halfway through if possible.
Spoon the beef and bean mixture over cooked rice in bowls. Top each serving with shredded cheddar cheese and sliced green onions.