Adjust oven rack to the middle position and preheat oven to 425 degrees F. Line a baking sheet with parchment paper or a Silpat.

In a large bowl, whisk together the flour, baking powder, salt, both sugars, cinnamon, nutmeg, and ginger.

Add in the cold butter, and using a pastry cutter or 2 forks, cut the butter into the flour mixture until the butter is evenly distributed throughout the flour mixture, and no large lumps remain.

In a small bowl, combine the pumpkin puree, egg, and half-and-half. Pour into the flour mixture, and fold to combine. Form the dough into a ball.

On a lightly floured work surface, pat the dough into a long rectangle, about 4x13-inches, and about 1-inch thick. Using a sharp knife, cut the dough into 3 equal pieces. Cut each of the pieces once, on the diagonal, to make 2 triangles. Do the same for the remaining pieces. You will end up with 6 large scones. For smaller scones, cut the long rectangle in half horizontally, and then follow the same steps thereafter.

Place the cut pieces of dough on the prepared baking sheet, leaving about an inch of space around. Bake for 14 to 16 minutes, until golden brown. Place on a cooling rack to cool completely.

In a small bowl, whisk together the powdered sugar, and milk until smooth. Using a pastry brusch, pain the glaze onto the cooled scones. Allow to dry for about 5 to 10 minutes, or until the icing is not wet before topping with the spiced glaze.

In a small bowl, whisk together the powdered sugar, cinnamon, nutmeg, and ginger. Whisk in the milk until smooth. Either drizzle the glaze on the dried plain glaze. Alternatively, I put the icing into a small ziplock bag and cut a small hole into one corner and used it as a piping bag to make the zig zag pattern on top.