Prepare the oven and pan. Preheat the oven to 425°F (218°C). Cover a baking sheet with parchment paper, or lightly grease a scone pan to keep the dough from sticking.

Combine the dry ingredients. Sift the all-purpose flour, granulated sugar, baking powder, salt, and 1 1/2 teaspoons pumpkin pie spice into a large mixing bowl or the bowl of a stand mixer. Stir until the ingredients are evenly distributed.

Incorporate the frozen butter. Grate the frozen butter directly into the flour mixture. Gently work the grated butter through the dry ingredients with your hands until no large pieces remain and the mixture develops a coarse, crumb-like consistency.

Prepare the wet mixture. In a separate medium bowl, whisk the pumpkin purée, half-and-half, and egg together until evenly blended.

Form the dough. Fold the pumpkin mixture into the flour-and-butter mixture just until a cohesive dough develops. Avoid excessive mixing. The finished dough should remain slightly sticky rather than becoming dry.

Shape the scones. Place the dough onto a lightly floured work surface and form it into a large round approximately 1 inch thick. Cut the round into 6 or 8 triangular wedges with a knife.

Bake. Arrange the scones on the prepared baking sheet or scone pan. Bake for 14–16 minutes, or until they develop a light golden-brown color. Remove them from the oven and allow them to cool before applying the glaze.

Prepare the cinnamon glaze. While the scones are cooling, whisk the confectioners’ sugar, milk, ground cinnamon, and 1/8 teaspoon pumpkin pie spice in a medium bowl until completely smooth. Adjust the amount of milk as needed to achieve the preferred glaze consistency, then allow the mixture to rest briefly so it can thicken slightly.

Glaze the scones. Once the baked scones have cooled, drizzle them generously with the cinnamon glaze. Allow the coating to set and firm before serving.