I had never heard of kabocha squash until they turned up in Spokane's mostly-organic grocery store, Huckleberry's. This is the best squash I've ever had. Very firm, dry flesh, with a delicious taste. I'm sure you could use it in your favorite squash recipe, but for those unfamiliar with squash, I have an extremely simple way to prepare it: I cut it in half (I cut parallel to the axis, rather than bisecting the axis; I have no idea if it matters) and scoop out the seeds and pulp, scraping the flesh well to get as much of the fibers of the central mass as I can. Then I place the halves, cut side down, in a baking dish with maybe 1/8 of an inch of water, but not more than 1/4 inch, in the bottom so the squash does not dry out while baking. Then I put it in the oven preheated to 425 F. for 40 minutes. Then I take it out, let it cool for a few minutes before handling, and then carefully scrape out the last of the threads from the central mass still clinging to the flesh. I don't use fats in cooking or in my food, but if you put butter on your food (a very unhealthy practice) you will enjoy butter on the squash. I eat it with catsup.
Catsup gets a bad rap. It's got tomatoes, vinegar, and high-fructose corn syrup in it. How can you go wrong? And it sure is healthier than butter, which is what most people put on it. But you can use gourmet home-made tomato sauce instead.
Kabocha is a local staple here in rural Japan. Its used for making soup, as a potato substitute, in salads, main dishes and even deserts. My favorite is BBQ'd but never with ketchup!