In a large skillet over medium-high heat, cook the ground beef until browned, breaking it up with a spoon as it cooks, about 5-7 minutes.
Drain excess fat from the cooked beef and transfer the beef to the slow cooker.
Add the chopped onion, chopped green bell pepper, and minced garlic to the slow cooker with the beef.
In a medium bowl, whisk together ketchup, tomato paste, 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 halfway through cooking.
After cooking, give the sloppy joe mixture a good stir and taste for seasoning, adjusting salt and pepper if needed.
To serve, spoon the beef mixture onto the bottom halves of the hamburger buns and top with the bun tops.
Serve immediately and enjoy your slow cooker beef sloppy joes.