Step 1Slice the kabocha into half-inch-thick half-moons. If the pieces are too large, cut them in half. Each piece should be about 2 or 3 bitefuls.
Step 2To make the batter: In a medium bowl, combine the ice water with the buckwheat flour and cornstarch. Whisk until mixture is combined. The batter will be slightly thin, sort of like syrup.
Step 3To make the kimpura: Heat the oil in a deep pot such as a Dutch oven or tempura frying pan (the oil should come up the sides of the pot about 2 to 3 inches), until a thermometer inserted reads 325 degrees.
Step 4Working in batches, dip the squash into the batter, letting the excess batter drain off so you don't have too much coating on the surface of the squash. Then deep-fry the squash, being careful not to crowd. Fry until the batter is crisp on all sides, about 2 minutes. Test a piece with a toothpick. If it comes out easily, it is done.
Step 5Drain the kimpura on paper towels. (It's best to stand the pieces, so they drain well.)
Step 6Arrange the kimpura on a plate. Serve immediately with salt or warm dipping sauce.