Add a layer of melted cheese to the patty and the hamburg sando becomes its richest member. The hamburg sando with cheese keeps everything that defines the baseline build, a soft beef-and-pork hamburg steak in dark sauce between white bread, and lays a melting slice across the hot patty so it slumps into the meat and the surrounding glaze. That one addition changes the register from savory-comforting to savory-indulgent, binding the patty, the sauce, and the bread into a single gooey, cohesive layer rather than three distinct ones.
The cheese is the variable, and how it is handled is the craft. The hamburg underneath is the standard Japanese hamburger steak: mixed ground beef and pork with sauteed onion and a milk-soaked breadcrumb panade, pan-cooked to a deep brown crust and a soft, juicy interior, then dressed in a demi-glace or a sweet ketchup-Worcestershire sauce. The cheese, usually a melty processed slice or a mild semi-soft type, is laid on the patty while it is hot, often briefly covered or passed under heat so it goes properly molten and drapes the sides instead of sitting as a cold rubbery sheet. The bread is soft shokupan, sometimes crusts trimmed, occasionally buttered or lined with cabbage to manage moisture. The balance to strike is real: cheese deepens the richness, so the sauce should stay savory and slightly acidic to keep the whole thing from going heavy and flat, and the cheese must actually melt to do its job of fusing the layers. Good versions show cheese threaded into the sauce and clinging to the patty, with the bread holding firm; weak ones use an unmelted cold slice that peels away in one piece, drown the build in sauce until it slides apart, or let the extra fat turn the bread greasy and slack underneath.
Eating it is the soft, oniony, deeply sauced experience of the base sando, made rounder and more lactic by the cheese, which adds a smooth, salty richness that coats the palate. It is the most filling and the most indulgent of the hamburg sandwiches, comfort food that leans fully into its own richness, with little textural contrast unless cabbage or lettuce is present.
Variations push the richness further or cut against it. A double cheese or a sharper cheese intensifies it; a fried egg adds another soft, rich layer; pickles, mustard, or extra cabbage introduce acid and crunch to lighten the load. Swapping sliced bread for a soft roll moves it toward the hamburg pan format. The broader Japanese yoshoku tradition of cheese-laced savory breads and filled bakery pan is a large field of its own, and it deserves its own article rather than being crowded in here.