Preheat the oven to 425 degrees F.
Place the squash in a medium saucepan and cover with cold water. Bring to a boil and simmer for about 10 minutes, or until tender. Drain and let dry over heat. It is very important to drain well, or the batter will be too liquidy. Mash squash with a potato masher and drain again, if necessary.
Stir in the sugar and then the mashed squash. Stir in milk, 1 tablespoon at a time, until you have a soft dough. With a wooden spoon, combine the dough thoroughly yet gently.
Turn dough onto a floured board and press down lightly until dough is about 1-inch thick. Using a scone cutter, cut out the scones and place on a lightly greased baking tray. It helps to flour the cutter each time.
Using a flour shaker, dust each scone with flour. Bake for 12 to 15 minutes, or until well-risen and golden brown.
Professional Recipe: This recipe was provided by a chef, restaurant or culinary professional and makes a large quantity. The Food Network Kitchens chefs have not tested this recipe in the proportions indicated and therefore cannot make any representation as to the results.
Recipe courtesy Mark Pearson, Roman Baths and Pump Room, England