In a large skillet over medium heat, cook the ground beef until browned, breaking it apart with a spoon as it cooks, about 6-8 minutes.
Drain excess fat from the cooked beef and transfer the beef to the slow cooker.
Add the chopped onion, green bell pepper, and minced garlic to the slow cooker with the beef.
In a medium bowl, whisk together ketchup, tomato paste, water, Worcestershire sauce, apple cider vinegar, brown sugar, chili powder, smoked paprika, salt, and black pepper until smooth.
Pour the sauce mixture over the beef and vegetables in the slow cooker and stir to combine.
Cover and cook on low for 6 hours, stirring once halfway through cooking.
After cooking, stir the sloppy joe mixture well and taste to adjust seasoning if needed.
To serve, spoon the beef mixture onto hamburger buns and serve warm.