Line a rimmed baking sheet with triple layer of paper towels. Spread pumpkin puree over towels. Press with second triple layer of paper towels until towels are saturated.

Peel off top layer of towels. Place second baking sheet inside first over pumpkin and flip. Remove top sheet and towels. Repeat if needed to reduce past to ⅓ cup.

Using a stand mixer fitted with paddle, mix flour, superfine sugar, 1½ teaspoons cinnamon, ginger, nutmeg, and salt on low speed until combined.

Add butter, 1 piece at a time, and mix until dough looks crumbly and slightly wet, 1 to 2 minutes.

Add pecans, pumpkin paste, 2 tablespoons cream cheese (1 ounce), and vanilla and beat until dough just begins to form large clumps, about 30 seconds.

Adjust oven rack to middle position and heat oven to 375°. Line 2 baking sheets with parchment paper.

Working with 1 disk at a time, roll dough to ⅛ inch thick between 2 large sheets of parchment paper. Transfer dough, still between parchment, to refrigerator and let chill for 10 minutes.

Bake 1 sheet at a time, until cookies are light golden brown, about 10 minutes, rotating sheet halfway through baking.

Let cookies cool on sheet for 3 minutes, then transfer to wire rack and let cool completely.

Whisk milk, remaining ½ teaspoon cinnamon, and remaining 1 tablespoon cream cheese (½ ounce) together in a bowl until combined.

Add confectioners’ sugar and whisk until smooth. Spread glaze evenly onto cookies (or drizzle) and let dry for at least 30 minutes before serving.