In a large bowl, whisk together the all-purpose flour, cinnamon, nutmeg, ginger, allspice, and baking powder until everything is evenly distributed. Next, add in both the brown sugar and white sugar, combining thoroughly to ensure there are no lumps and the mixture is evenly mixed throughout.
Add the cold, diced unsalted butter to the dry ingredients. Use a pastry cutter or two forks to work the butter into the mixture until it resembles coarse crumbs. This will help ensure flaky scones. I always make sure the butter is really cold, as that gives the scones their perfect texture.
In a separate bowl, whisk together the large egg and vanilla extract. Then, add the pumpkin puree and heavy cream (or half & half) and mix until the wet ingredients are fully combined and smooth.
Pour the wet ingredients from Step 3 into the dry mixture with butter from Step 2. Gently mix until a sticky dough forms. Tip the dough onto a lightly floured surface and knead gently, using a little extra flour as needed to keep it from sticking. Work it just enough for the dough to come together and become smooth.
Shape the dough into an 8-inch circle on the floured surface. Using a sharp knife, cut the circle into 8 equal triangles. Place the triangles on a baking sheet lined with parchment. Bake in a preheated oven at 425°F (220°C) for 13 to 15 minutes, or until lightly browned and baked through.
In a small bowl, combine instant coffee granules with 4 to 5 teaspoons of milk and stir until dissolved. Transfer this coffee mixture to another bowl containing the powdered sugar. Whisk until smooth and pourable. Drizzle the glaze generously over the cooled pumpkin scones. To give the glaze a little extra richness, I sometimes use half & half instead of milk.