The traditional Japanese version is simply a boneless pork chop, battered out a little thinner, they then pané the chop (passing through flour, then egg, then panko breadcrumbs) and deep fry or shallow fry but in deeper oil than perhaps under normal circumstances. They then serve simply as per the picture with very finely shredded Chinese leaf, and some Tonkatsu sauce. I'm not sure if I prefer the sauce on the meat or on the leaves, so usually end up with both!
The reason I've called it "kind of" Tonkatsu is because we had it as a family for the first time, and one of my daughters suggested that it would be nice with mozzarella cheese inside. Of course, their wish is my command under all circumstances (?!?!) so I thought I'd give it a go. Having had some interesting experiences with stuffing various cuts of meat, usually ending up with the need to cover my creation with sauce due to the explosion of molten cheese, I thought about encasing the cheese in another of my favourite things. Parma ham.
Whether you use mozzarella, cheddar, or any other decent melting cheese is entirely up to you. Worth trying it without as well, the Japanese do know a thing or two about what tastes good. Just make sure you either make or buy some Tonkatsu sauce as it really makes the dish come alive. I'll post two recipes for the sauce, which if you make, then combine, it works brilliantly.