In a skillet over medium heat, brown the ground beef with the diced onion and green bell pepper until the beef is no longer pink. Add the minced garlic in the last minute of cooking. Drain any excess grease.
Transfer the beef mixture to the Crock Pot. Stir in the ketchup, tomato sauce, brown sugar, Worcestershire sauce, yellow mustard, apple cider vinegar, salt, and black pepper until well combined.
Cover and cook on low for 4 hours, stirring occasionally to prevent sticking and to ensure even cooking.
Serve the Sloppy Joe mixture piled onto hamburger buns, optionally accompanied by a side of coleslaw or pickles.