I live in the land of kabocha, so I have used it a lot. I have used it in my curried pumpkin soup recipe and it is a family favorite--really yummy. I use Kabocha pretty much in place of pumpkin. In recipes that call for canned pumpkin, I actually peel it, cut it in chunks, and then steam/boil it in the microwave until it is soft and then I mash it it up and use a bit of the left over water to add to make it the consistency/wetness of how I remember mashed pumpkin.
A quicky recipe that my toddler likes is this. Don't peel it, but thin slice it into halfmoons. Steam it until you can insert a fork easily but it is still firm. Make a dressing of about say 1 part soy sauce to 2 parts rice vinegar. Pour it over the kabocha in a dish, and sprinkle with sesame seeds. A great finger food and actually tastes best at room temperature.