Preheat the oven to 425°F (218°C) and line a baking sheet with parchment paper or lightly grease a scone pan.
In a large bowl, sift together the flour, sugar, baking powder, salt, and pumpkin pie spice, then stir to combine.
Grate the frozen butter into the dry mix and gently blend with your fingertips until it looks like coarse crumbs.
Whisk the pumpkin puree, half and half, and egg in a separate bowl until smooth, then fold into the dry mixture just until combined—don’t overmix.
Turn the dough onto a lightly floured surface, shape it into a 1-inch-thick round, and cut into 6–8 wedges. Arrange on the prepared sheet and bake for 14–16 minutes until light brown. Cool completely.
For the glaze, whisk together confectioners’ sugar, milk, cinnamon, and pumpkin pie spice until smooth, adjusting the milk for desired consistency.
Drizzle the cooled scones with the glaze and let it set before serving.