Wash the squash and prick it with a fork. Bake the whole squash at 350° until tender. Halve cooked squash and remove seeds and fibers. Scoop out meat with a spoon and put it in a large bowl. Using a potato masher, mash squash meat to a purée; a few small chunks might remain.
Measure 2½ cups purée and return to bowl. Add semolina, egg, salt and spices; mix well.
If you like, preheat oven to 250°F to keep latkes warm. Line a plate with paper towels.
Heat 3 tablespoons oil in a medium or mediumlarge nonstick skillet over medium-low heat. Take 1 heaping tablespoon batter, push it off spoon with a rubber spatula into hot oil and gently flatten and smooth the pancake with bottom of spoon. Add more pancakes to skillet, leaving room to turn them over.
Fry latkes about 2 minutes, or until golden brown on bottom. Turn them carefully using 2 pancake turners. Fry second side until golden. Transfer to a lined plate.
Make more latkes from remaining batter.
Serve hot on a platter garnished with mint sprigs; accompany with cranberry apple chutney and yogurt.