Preheat oven to 375°F (190°C) and line 2 baking sheets with parchment. Beat the 1/2 cup butter, 3/4 cup granulated sugar, and 1/4 cup brown sugar on medium speed for 3 minutes until pale and fluffy.

Add the 1 large egg yolk, 1/3 cup blotted pumpkin puree, and 1 tsp vanilla extract. Mix on medium for 30 to 60 seconds until combined.

Whisk together the 2 1/4 cups flour, 1/2 tsp baking soda, 1/2 tsp baking powder, 1 1/2 tsp pumpkin pie spice, 1/2 tsp cinnamon, and 1/2 tsp salt. Add to the wet ingredients and mix on low just until no dry streaks remain, about 45 seconds.

Scoop the dough into 8 balls (about 3 tbsp each), flatten to 3/4 inch thick, and bake at 375°F (190°C) for 11 to 13 minutes until edges are set and tops are matte. Cool on the pan for 5 minutes, then transfer to a wire rack to cool completely.

Beat the 8 oz cream cheese and 1/4 cup butter on medium-high for 2 minutes until smooth. Add the 1 1/2 cups sifted powdered sugar, 1/2 tsp cinnamon, and 1 tsp vanilla. Mix on low 30 seconds, then medium for 1 minute until thick and creamy.

Swirl about 3 tbsp frosting onto each cooled cookie with a spoon or offset spatula, dust with a pinch of cinnamon or pumpkin pie spice, and serve at room temperature.