While kabocha is pumpkin-shaped, it doesn't turn orange and is hard, like a butternut squash. Definitely not a Jack-o-Lantern pumpkin! It has orange meat, is sweeter than a butternut squash and has a texture almost like a potato. When the skin is shiny and green is the best way I can tell if it's ripe. You can buy them in most grocery stores and any Asian market.
A friend of mine requested a kabocha recipe. Here's the 'recipe' according to my mom, and thanks for writing!
Water (or dashi)
Cut the kabocha in half, then quarters, then in half lenght-wise so you get 'fat-triangle' shaped pieces. Remove seeds and stringy stuff. Put kabocha pieces in the bottom of a dutch oven or similar pot. Add about 1 inch of water (or dashi). Mom says it's VERY IMPORTANT that you don't cover the kabocha with water. Sprinkle lightly with brown sugar and a bit of shoyu. If you are using dashi, be very light with the shoyu. Poach (cook on a very low boil) until tender.
Mom says you can also slice kabocha thinly (as you would a melon) and fry it tempura-style, or saute with a little butter, brown sugar and shoyu.