How to Make It
Preheat the oven to 400°. Cut the squash in half lengthwise, scoop out and discard the seeds, and place on a baking sheet, cut-side down. Pour about 1 cup water around the squash and bake until the squash is tender when pierced with a knife, about 45 minutes. (Check the water halfway through baking; if it has evaporated, add some more.) Remove the squash from the oven and set aside to cool. Once the squash is cool, scoop out the flesh and put in a blender.
Meanwhile, combine the sugar and 2/3 cup water in a small saucepan. Cook, stirring gently with a wooden spoon, until most of the sugar is dissolved. Brush down the sides of the pan with a wet pastry brush and bring to a simmer. Add the ginger, cinnamon, peppercorns, cloves and nutmeg. Cover and simmer gently for 2 minutes. Remove from the heat and let cool, uncovered.
Pour the cooled syrup through a fine-mesh strainer into the blender. Discard the spices. Add the cider and maple syrup and blend until smooth.
Freeze the mixture in an ice cream machine according to manufacturer's directions, then transfer to an airtight container and put in the freezer to harden, at least 3 hours.