I assume there are more kinds of vegetables in Japan than in Europe. Especially than Central Europe. Japan can be a country which you do not have to eat meat during the tour. In Europe, the dish without meat/fish is categorized as vegetarian dish, but not in Japan.
Major ways to eat vegetables are fried, deep fried, stewed, grilled, boiled, steamed and of course raw. For example, vegetable tempura, hot pot such as sukiyaki and shabushabu, Japanese style BBQ and miso soup. Raw sliced cabbage is always accompanied for Japanese style schnitzel, tonkatsu. Then, grilling vegetables together with meat is normal.
However, not all vegetables are eaten by deep fried. Eggplant and pumpkin can be deep fried but never deep fries tomato, cabbage and cucumber. These three vegetables cannot be found in miso soup either. On the other hand, eggplant and pumpkin are not for the suikiyaki hot pot.
Then, not so many restaurants or diners offer a bowl of salad as a main dish. Salad is usually considered as side dish but almost all dishes are with vegetables therefore may be you will not feel you are lack of vegetables during your stay in Japan.