The pizza hot sando is the format borrowing a flavor profile and reproducing it in miniature inside a clamped iron. It takes the sealed-pocket structure from the baseline hot sando and fills it with the trio that signals pizza to a Japanese palate: tomato sauce, melting cheese, and ham, sometimes with green pepper or a few rings of onion. The result is not pizza and does not pretend to be. It is a pressed sandwich that delivers the tomato-and-cheese sensation in a toasted bread shell, which is exactly why people make it and why children especially like it.
The interesting craft problem is the tomato sauce, because it brings both acidity and water into a format that punishes excess moisture. The sauce has to be thick, more like a paste or a reduced pizza sauce than anything pourable, spread thin and kept well short of the crusts. The cheese sits on top of it and does the structural work, melting under the press into a binder that holds the sauce and ham together so the filling has enough body to survive a clean cut. The seal then matters more than usual: hot tomato sauce is liquid and acidic and will find any gap in the crimp and stain the plate red. A good pizza hot sando cuts to show a tidy stratum of glossy sauce and molten cheese with the ham folded through, the toasted shell providing the crisp counterpoint that a soft pizza crust never would. A poor one is a wet, orange-bleeding mess where a thin sauce soaked the crumb, or a scorched parcel where the cook overheated it trying to set a too-juicy filling. The inside should be hot and the cheese fully molten, the sauce reduced rather than weeping.
Variations stay inside the pizza idiom: pepperoni or salami in place of plain ham, a scatter of corn or green pepper, a heavier hand with the cheese for a stretchier pull. Some cooks finish the outside with a brush of garlic butter to push the pizzeria association further. That garlic-buttered, herb-dusted treatment becomes a noticeably different thing, and it is enough of a distinct experience that it deserves its own article rather than being crowded in here.