Preheat the oven to 425 degrees F. In a food processor, pulse the flour, baking powder, baking soda, salt, cinnamon, nutmeg, ginger, cloves, brown sugar, and granulated sugar until well blended. Add the cold butter and pulse in short bursts until the mixture looks like coarse crumbs with no large butter pieces visible. Transfer the mixture to a large bowl and make a well in the center. If you do not have a food processor, whisk the dry ingredients by hand and use a pastry cutter to work in the butter.

In a separate bowl, whisk the chilled pumpkin puree, buttermilk, egg, vanilla extract, and honey until smooth. Pour the wet ingredients into the well in the flour mixture and stir with a wooden spoon until the dough starts to come together.

Turn the dough out onto a lightly floured surface and knead it gently just until it holds together. Pat it into an even 8-inch round and cut the round into 8 equal wedges with a large knife. Dust the knife with flour as needed because the dough will be sticky.

Arrange the wedges on a parchment-lined baking sheet. Brush the tops with the 1 tablespoon half and half and bake for 13 to 15 minutes, until the tops are golden brown and a toothpick inserted in the center comes out clean. Transfer to a wire rack and cool for 10 minutes before glazing.

Whisk the powdered sugar and 2 tablespoons half and half together in a small mixing bowl until smooth. The glaze should be thick but spreadable; add a tiny bit more half and half if needed. Spoon the glaze over the scones and spread it evenly over the tops, using all of it, then let it set at room temperature.

In another bowl, whisk the powdered sugar, pumpkin puree, cinnamon, nutmeg, ginger, and 1 tablespoon half and half until smooth. If the icing is too thick, add water a few drops at a time.

Spoon the icing into a small zip-top bag, seal the bag, and snip off a tiny corner. Drizzle the icing over the glazed scones and let it set before serving.