I recently made a wonderful curried butternut kabocha squash soup. i cut the squash into bite size pieces and roasted until tender before adding to the soup. it was totally vegan to and probably the best soup i've ever made. i left it chunky instead of pureing it like most squash soup recipes have you do.
it is also the only winter squash i have sauteed. i sliced it into thin wedges and sauteed it with sweet yellow onion and rosemary -wonderful!
the hardest part ir peeling it! what a pain!
My favorite squash in the world and one I use to make the simplest (3-4 ingredients) most delicious soup in the world (25 minutes start to finish and only 5 or so minutes hands-on):
1) Wash the squash and only peel off any white bumpy parts. The skin is delicious and totally edible!
2) cut it in half, scoop out the seeds and cut into chunks.
3) place the chunks in a pot and pour in water to almost cover.
4) Add a good amount of soy sauce (at least half a cup, depending on size of squash), lots of thicky sliced fresh ginger, and if you like one cut up onion. My Japanese friend also uses kombu, I don't.
5) Bring it to a boil and simmer it until squash is tender. take out or leave the ginger as you like.
This is a hearty, flavorful peasant soup. It is delicious right away as well as for several days as the flavors intensify. I serve it with rice for a full meal.
A friend of mine also swears by kabocha tempura though I've never tried it
With an unfamiliar squash, especially one that is renowned for its sweet dense taste, the simplest method is often the best start so you can get an idea of its real taste. A Japanese lady I was giving English lessons to told me she would cut it in half, scoop out seed stuff, cover w/ parchment or wax paper and just microwave till tender (basically a dry steam effect)- then it was scooped out and enjoyed along with other meal ingredients. I like it that way as well, sprinkled w/ a nice crunchy salt to off-set the sweetness.