I am assuming these are Kabocha squash---it seems to be the closest thing I could find to it. I am using them accordingly.
Kabocha squash are often called a Japanese Pumpkin. They're smaller than pumpkins (at least the ones we're used to carving) and have a lot of green on them. However, they can be used in any recipe that calls for pumpkin or butternut squash (I love the interchangeability of vegetables!).
I went ahead and processed mine yesterday. I didn't have a good storage place for them and was worried about them going bad. Kabocha squash likes to be at a warm temperature (like the temperature of my house in the summer) for the first couple of weeks and then at a cooler temperature (between refrigerator temp and "room"--68 degrees--temperature). I don't have that in my house, so I couldn't completely ripen the Kabocha. One of my kabochas did go bad--rotted and grew mold around the stem, so I wanted to process them before I lost any of my others. I thought about cooking with them now, but the thought of lots of "winter" (called winter squash because hypothetically they'll keep part of the winter) squash in 90 degrees weather wasn't appetizing to me. Curtis and I are having fun dreaming up our root cellar we want to dig in our backyard to help the summer/fall vegetables like potatoes and squash last longer. Won't happen, but one can dream.
The easiest way to process (or preserve) any pumpkin-like squash, which includes pumpkins, butternut squash, and kabocha, is to cook, puree, and then freeze them. They are difficult to remove the shell/skin from. Here's what I did. I cut the squash and half and removed the seeds. (middle picture) The seeds can be difficult to scoop out with a spoon so I use a grapefruit knife (or spoon) or any utensil with a serrated edge, even the utensil I use to spread frosting on cakes. Then, I cut the halves in very large chunks. I steamed them for 30 minutes to an hour. Once the flesh was easily pierced with a fork, I removed them from the steamer (steamed squash--bottom picture) and cut the shell off of them. I put the chunks in freezer containers and mashed them with my pastry blender (I use my utensils for many purposes, it prevents me from buying too many individualized tools!).
In the past, I also boiled the squash down in a little bit of water. That works too. However, frozen squash tends to get a little liquidy when thawed so I wanted to avoid putting any extra water in. Thus, I steamed them. We'll see how it works when I pull it out of the freezer to make butternut (kabocha) squash bisque or pumpkin (kabocha) chocolate cheesecake.