Put ground beef, onion, and garlic in a 6-quart slow cooker. Cover and cook on high for 1-2 hours, stirring occasionally until the meat is cooked through and crumbled. (A mix-and-chop like this one helps to break the meat up easily.)
Add the ketchup, brown sugar, and Worcestershire sauce to the meat mixture. Stir well to mix. Cover and continue cooking on high for 15-30 minutes until heated through.
Add the cubed Velveeta. Stir to incorporate. Cover and continue cooking on high for 30-60 minutes, stirring occasionally until cheese is melted.