Only time I worked with it, almost hurt myself trying to peel the darn thing.
Yes, kabocha is the worst. My only suggestion is to pop it into the microwave for about 5 minutes, then let it cool. That seems to help a bit. Also, figure out ways to cut on a straight line, down from top to bottom (holding the bottom firmly on a cutting board), as much as possible. And of course I don't need to tell you to sharpen you knife! (Do not bother trying to peel it with a peeler. Even the best peelers are no match for it.) Good luck! ;o)
I don't peel kabochas anymore. You don't need to because the skin cooks to tenderness like the flesh of the squash. So leave it on and consume with the rest of the kabocha.
I don't peel them either. I usually braise them in a smokey/sweet dashi (http://food52.com/recipes...) and choose to eat the peel or leave it depending on the texture. They are also magical in soup as they get so velvety. I roast wedges of them with a cubed sweet potato, shallots and garlic and blend it all up with veggie or chicken broth and sometimes a bit of chipotle.
Traditionally Japanese cooks don't peel the skin off of kabocha either. It becomes tender and it's fine to eat. But if you really want to peel it, perhaps you can cut into cubes first then using chef's knife, trim away the skin on cutting board.
So thrilled to see the support for not peeling this great squash. I have found a number of veggies like this-that don't need peeling. Beets and Sunchokes are others i don't peel. (And higher concentration of the nutrition is in a vegetable's skin)
I do peel it at home. A sharp chef (or similar type) knife works well. I usually cut one side so there is a flat surface to the board. And then I cut off the skin from the top down to the board. Never had a problem with getting the skin off that way.
I've never bought any whole kabocha so far. And since it usually comes quartered at my supermarket here in Japan, I just rinse it and place it in a steamer before cutting them into smaller pieces or getting rid of the skin. I don't know what it is called but the glass steamer in the shape of a fuji-san comes in pretty handy.