Preheat the oven to 400ºF and line a baking sheet with parchment paper.
In a large mixing bowl add the flour, baking powder, sugar, salt, cinnamon, and pumpkin spice and mix together.
Add the cold butter to the mixing bowl and cut it into the flour mixture until it resembles fine breadcrumbs.
In a separate bowl add the egg, milk, and pumpkin puree and whisk together.
Pour the wet ingredients into the dry ingredients and briefly mix until a dough starts to form. Do not over mix.
Lightly flour a work surface then turn the dough out on to it. With lightly floured hands work the dough into a ball then use the palm of your hand to flatten it into a disc of about 8 inches. Be careful not to over-handle the dough.
With a sharp knife, cut the dough into 8 triangles. It will be quite sticky and that’s fine.
With lightly floured hands transfer the dough triangles on to the prepared baking sheet and brush the tops with the 1 tablespoon milk. Leave some space in-between the scones - you may need to use two sheets.
Bake in the center of the preheated oven for 15 minutes, or until the scones are light golden brown. Transfer to a wire rack and cool for 10 minutes.
Meanwhile, to make the white glaze, add the powdered sugar into a small mixing bowl and slowly pour in the milk while mixing. The glaze should be thick and pourable but not runny.
Use a spoon to spread the glaze in an even layer on top of each scone then leave to set for a few minutes.
Meanwhile, to make the spiced pumpkin glaze, add the powdered sugar, pumpkin puree, and pumpkin spice into a small mixing bowl then slowly add the milk. The glaze should be thick and pourable but not runny.
Transfer the spiced pumpkin glaze to a piping bag and then snip the end off with a pair of scissors. Drizzle it over each scone.
Glazes: If either of your glazes are too thick gradually add a few drops more milk. If too thin, add a little more powdered sugar until the desired consistency is reached.