In a large mixing bowl, combine flour, baking powder, salt, baking soda, cinnamon, ginger, nutmeg, cloves, and brown sugar, ensuring everything is mixed well and any clumps of sugar are broken up.
Cut the cold, cubed butter into the flour mixture using a pastry blender until the mixture resembles coarse crumbs with pea-sized bits of butter.
In a separate measuring cup, whisk together the pumpkin puree, cream (or buttermilk), and one egg.
Create a well in the center of the dry ingredients and pour in the liquid mixture. Stir until just combined, leaving the dough somewhat shaggy.
Transfer the dough onto a floured surface and shape it into a rough rectangle. Fold the rectangle in thirds, like folding a letter, and then reshape and fold again. Don’t worry about perfection.
Cut the dough into two halves and flatten each half into 6-inch diameter rounds, about 3/4-inch thick. Slice each round into 8 wedges and place them on prepared baking sheets, spaced about 2 inches apart. Freeze the scones while preheating the oven.
To make ahead: The unbaked scones can be refrigerated overnight or frozen for up to one month. When baking from frozen, increase the baking time by about 2 minutes.
Preheat your oven to 400°F and position the oven rack in the center. Line two baking sheets with parchment paper.
In a small bowl, mix the remaining egg with 1 teaspoon water. Brush this mixture over the chilled scones.
Bake for 12 to 15 minutes, or until the scones are golden brown. Remove from the oven and cool on a rack while you prepare the glaze.
For the glaze:
In a small bowl, mix the powdered sugar, pumpkin puree, milk, and cinnamon with a fork until smooth. Drizzle the glaze over the scones. If needed, add a little more milk to achieve a dipping consistency. Allow the glaze to set before serving.
These scones are best enjoyed fresh out of the oven.