Heat a large skillet over medium-high heat. Add the ground beef and cook until browned. Instead of breaking it into tiny crumbles, leave some larger pieces so they can soak up the sauce.
Add the diced onion to the skillet and cook for 4–5 minutes, stirring occasionally, until softened and translucent.
Stir in the ketchup, tomato sauce, Coca-Cola, Worcestershire sauce, brown sugar, garlic powder, onion powder, smoked paprika, salt, and black pepper. Mix until everything is well combined.
Bring the mixture to a gentle simmer. Reduce the heat to low and let it cook for 10–15 minutes, stirring occasionally, until the sauce has reduced and thickened.
Once the sauce is thick and glossy, stir in the cubed cheddar cheese. Continue stirring until the cheese is melted and fully incorporated into the sloppy joe mixture.
While the cheese melts, butter the hamburger buns and toast them until lightly golden
generously spoon the Coca-Cola sloppy joe mixture on top. Serve immediately and enjoy!