Press the pumpkin between paper towels to blot out excess water until thicker and drier.

Whisk the flour, pumpkin pie spice, cinnamon, baking powder, and salt in a bowl.

Beat the butter and sugar until light, about 2 minutes. Add the blotted pumpkin, egg, and vanilla and mix until smooth, then mix in the dry ingredients just until a soft dough forms.

Divide the dough in two, flatten into disks, wrap, and chill at least 1 hour.

Roll one disk to about ¼ inch thick on a lightly floured surface. Cut with a pumpkin-shaped cutter and lift the shapes onto parchment-lined sheets.

Chill the cut cookies on the sheet 15 minutes so they hold their edges.

Preheat the oven to 350°F and bake 9 to 11 minutes, until the edges are just set but still pale. Cool on the pan 5 minutes, then transfer to a rack to cool completely.

Whisk the confectioners' sugar with the corn syrup, vanilla, and milk one tablespoon at a time until smooth and pourable but not runny. Stir in orange gel coloring to the shade you like.

Spread or pipe the icing onto the cooled cookies, nudging it to the edges. Let set firm, about 2 hours, before stacking.