The cheese dog is the hot dog's argument that a sausage and a soft roll are improved by something molten running through them. In its plainest Japanese form it is a steamed or griddled sausage in a split bun with cheese melted over or tucked alongside, the kind of casual hand food that fills convenience cases and bakery warmers. A second, louder version runs through Korean street food: a corn-battered dog on a stick, the interior part sausage and part stretchy cheese, deep-fried until the coating crackles and the core pulls into long threads. Both share the same simple promise, which is salt, fat, and the small theater of cheese that moves when you bite it.
The bun version lives or dies on heat management and the cheese itself. The sausage should be juicy and snappy, the roll soft enough to fold without tearing, and the cheese chosen to actually flow rather than seize into a rubbery cap. A good one has cheese that has gone properly liquid against a hot sausage, a bun that is warm through, and a balance where the dairy rounds the salt instead of burying it. A sloppy one is a lukewarm sausage with a cold slab of cheese laid on top like a coaster, the whole thing neither melted nor crisp. The battered stick version asks for a different discipline: a fry-stable cheese that survives the oil, a batter that sets golden without going greasy, and a clean break between crust and pull when you bite.
The genre spreads quickly once you allow toppings. Ketchup and mustard in stripes, a roll in sugar for the corn-dog style, furikake or shredded cabbage in the bakery style, a chili-and-cheese load that turns it into a fork affair. The mozzarella-heavy Korean street version and the bakery sausage roll have drifted far enough apart in technique and texture that each deserves its own article rather than being crowded in here.