Kabocha squash is that large, dark green squash that looks like a small pumpkin, only it's dark green. :) Look at this though - it's very orange on the inside! It's really velvety and quite sweet. I've tried roasting and eating the seeds too, but I don't care for them. The only two ways I've had this, is as tempura (Japanese) and this soup. I like smooth soups, but I also heard just today from someone else who said her grandmother just cubes it and drops it into a pork soup, which sounds good too! I'll have to try that next time. Also, since it's on the sweeter side, you could totally play that up and use it something like a pie, or roast it with some butter, cinnamon & sugar ... or whatever.
This is what it looks like on the outside.
You can peel it, then steam it or boil it, but it's a really hard squash, so be careful - don't cut yourself. I just cut it up like this, and then boil it (with a bit of salt) with rind on and wait to scoop it out once it's cooked and soft. 
Boil until soft (about 20 min or so). Scoop out the orange flesh, and discard the rind.
Finishing the soup:
In a blender, combine the cooked Kabocha with vegetable or chicken broth (you can make the soup as thick or as thin as you like - I used about 3 cups for one medium sized squash and it was about milkshake consistency). I also added about 2 TBSP of butter, and then salt & pepper to taste, a squeeze or two of fresh lemon to taste, and then a pinch of dried thyme. Blend until completely smooth and then return to a pan to reheat. You can finish it by adding a splash of cream or half & half, if you want.
