Heat the butter in a large skillet over medium-high heat.
Add the diced onion and cook until softened.
Add the ground beef and season with salt and pepper, stir in the minced garlic.
Cook for 6 to 8 minutes, breaking up the meat with a wooden spoon, until browned.
Transfer the beef mixture to the slow cooker.
Add the tomato sauce, ketchup, brown sugar, Worcestershire sauce, garlic powder, onion powder, mustard, and smoked paprika. Stir to combine.
Cover and cook on high for 3 hours or low for 6 hours.
Spoon the sloppy joe mixture onto hamburger buns.
Top with a slice of yellow cheese and serve warm.