Step 1Heat the oven to 300 degrees. Peel and seed the kabocha squash and cut it into about 1-inch cubes. You should have 3 cups of cubed squash.
Step 2In a heavy-bottomed sauce pot, melt the butter and add one-half cup sugar, squash and 3 tablespoons water and bring to a simmer; then turn the heat to low and cover. Make sure to check the squash frequently and stir until the mixture is a puree, about 30 minutes. You should have 1 cup puree.
Step 3Meanwhile, mix the cream, eggs, yolks, 1 cup sugar, vanilla and pinch of salt. Let stand 1 hour.
Step 4Take the remaining 1 cup sugar and, in a heavy-bottomed sauce pan over high heat, melt the sugar and cook it until it caramelizes to a deep amber color, 5 to 10 minutes. Pour the caramelized sugar evenly into the bottom of a bread loaf pan, and let cool 5 minutes.
Step 5Pass the cooked squash through a fine sieve. Add 1 cup of the strained squash to the cream mixture. Mix well, then pour into the loaf pan.
Step 6Place the loaf pan into a larger baking dish. Fill the dish with hot water, about 1 1/2 inch high around the loaf pan, and bake 1 1/2 to 2 hours, until the creme caramel is set and the center has a slight jiggle.
Step 7Let cool 1 hour on a wire rack, then cover and chill overnight. When you are ready to unmold the creme caramel, loosen the sides with a small spatula. Dip the loaf pan into a pan of hot water to loosen the bottom and sides. Invert onto a serving platter.