Nasu dengaku, is the traditional name of this famous Japanese dish. Eggplants are lacquered with miso and put in the oven, so that the eggplant become wonderfully soft and the miso caramelizes nicely.
Mirin is wine rice, but it's not sake. It's a sweet condiment, but it's often used in savoury Japanese dishes. You can find it in ramen bowls and seafood recipes, teriyaki sauce and even some sushi types.