Preheat oven to 425°F. Line a baking sheet with parchment paper.
Bring a medium saucepan of water to a boil, add some salt, and cook the squash for 3 minutes. Drain and cool. Reserve.
In a large bowl, whisk together the flour, sugar, baking powder, 1/4 teaspoon salt, and nutmeg. Add the butter and cut it into the flour with a pastry blender until it resembles cornmeal, but you also want to keep some of the butter in pea-sized pieces, which will create the flakiness in your scones. Fold in the cooled squash and chocolate.
In a small bowl, mix together the eggs and half and half. Add this mixture to the dry ingredients and mix to combine.
Turn the dough out onto a floured surface to do the gentle kneading. You are really just turning the dough over on itself; using a bench scraper is very handy to get this done without overworking the dough. Turn the dough 12 times.
Roll the dough into a log and cut it into 8 equal pieces. Place on the prepared baking sheet. Brush the top of the scones with the cream and sprinkle generously with sugar. Bake until set in the middle and golden, about 30 minutes. Allow to cool on the pan before removing to a wire rack.