I try to make every effort to explain what the very Japanese ingredients are in Japanese bentos and recipes. But this comment by Sophie  made me realize that even ingredients that may seem familiar in principle, may be a bit of a mystery when they are used in bentos. Here’s her question:
..when I saw the parmesan cheese in the bento , I just had to ask: Americans (especially me!) love cheese. We put it on everything we can. Usually it’s American cheese, or cheddar or mozzarella. I have a couple recipes from bento cookbooks that say to use a “slice of cheese” like in rolled up tamago or hampen and cheese. What kind of cheese are they expecting me to use? Is there a Japanese favorite? Or did these cookbooks just make these recipes up to appeal to the American obsession with cheese?
The short answer is: no, the cheese reference is not just there for Americans - Japanese people love cheese too. When just ‘cheese’ is specified in a Japanese cookbook, it usually means presliced, processed cheese, just like the kind you get in the U.S. and elsewhere, individually wrapped in plastic. Japanese sliced cheese is a bit firmer than American sliced cheese, but you can use American sliced cheese in the same way.
Delving into the history of cheese in Japan a bit may clarify things further. While there is historical evidence of a cheese-like curd product having been made and eaten in Japan as early as the 12 or 13th century, serious cheese production only started in the 1930s or so. At the time, Japanese people were not familiar with the texture or flavor of cheese, so cheese manufacturers like Yukijirushi or “Snow Brand” (who is still a major manufacturer of cheese and dairy products) made cheese that resembled foods that were more familar, like kamaboko (firm fish paste cake). The standard processed cheese sold by Yukijirushi didn’t even melt when heated - it softened a bit, but retained its shape, rather like haloumi cheese does. A second type of processed cheese was specifically sold as ‘cheese that melts’, for use on pizza, cheese on toast, and the like. I remember these cheese types being sold when I was a kid, but I don’t think they are available as such anymore, although you can buy ‘pizza cheese’, which is a kind of processed mozzarella.
Nowadays, all kinds of cheese are available in Japan, both imported and made domestically; imported cheese is terribly expensive however. When it comes to bentos that you see online or in most Japanese bento cookbooks, usually only processed cheeses are used. The way presliced cheese is used in charaben is really similar to the way other firm yet easy to cut products, like kamaboko, hanpen (a puffy light fish paste product made from fish paste and whipped egg whites), ham, wiener sausages and fish-paste or gyoniku sausage.
Another type of processed cheese product that makes its way into bentos is ‘candy cheese’. This is just little chunks of processed cheese that are individually wrapped to look like candy - and thus theoretically appeal to picky-eater kids. I’ve even seen these featured prominently in a translated-to-English bento book. As far as I know ‘candy cheese’ is not available outside of Japan (unless it’s available in other Asian countries?)…so I can imagine the ‘candy cheese’ confusing quite a few readers of that book.
The last type of cheese that may appear in a bento cookbook is kona cheezu or ‘powdered cheese’. This is the pre-grated stuff that comes in a green canister. (Yes, this is the era of multinational brands.)
Of course, in your bentos you can use any cheese you like. Personally I prefer to stay away from processed cheese, purely for taste reasons.
If for some reason you can’t get a hold of malleable presliced processed cheese, but want to make cheese cut-outs and such for your bentos, I’ve tried the following cheeses with varying degrees of success:
Incidentally, while Japanese people probably don’t eat as much cheese as Americans, I’d actually rank the American fondness of cheese below that of most European nations. There is a blog called Chez Loulou , whose owner Ms. Loulou is attempting to eat every French cheese there is in existence. She’s almost up to no. 170, but still has a long, long way to go! In Switzerland, it’s not at all uncommon to just have cheese and bread or potatoes for dinner, and there’s also fondue and raclette. (We once served a meal consisting just of several varieties of cheese, with wine and bread, to an (older) American friend who was visiting. He later confessed that up until then he would have never dreamed of just having cheese and bread for dinner - to him that was a ‘poor person’s meal’!) There are tons of local cheeses in Italy, Spain, the UK… and on and on.
Do you like to use cheese in your bentos - and if so, what are your favorites, and how do you use them?