You can use Kabocha basically the same as any hard yellow squash. You can use them instead of pumpkin and they store (whole) better than pumpkin!
If you just want to use the flesh, typically easiest to just microwave. There are different ways, I prefer to scoop out the seeds and guts first, poke with a fork, wrap in plastic and just cook 3 or so minutes at a time until I get where I want to be...
For something very different, the vegan Vietnamese place we go to does a version of this soup using Kabocha:
https://www.youtube.com/watch?v=mM61C0hCxlc