In a kitchen mixer, combine the softened butter, granulated sugar, brown sugar, and pumpkin spice. Mix on medium-high speed until well blended and creamy.

Add the pumpkin puree, egg, egg yolk, and vanilla extract. Mix on low speed until just combined.

In a separate bowl, whisk together the all-purpose flour, corn starch, baking powder, and salt.

Gradually add the dry mixture into the wet ingredients while mixing on medium-low speed. Stir until just combined.

Cover the dough with plastic wrap and refrigerate for 1 hour.

Preheat the oven to 350°F and line baking sheets with parchment paper.

Remove the dough from the refrigerator and roll it into 2 tablespoon-sized balls, placing them on the prepared baking sheets.

Bake the cookies in the preheated oven at 350°F for 12-13 minutes until the edges are set and the tops are lightly golden.

After baking, gently flatten each cookie with a clean glass while still warm on the baking sheet.

Allow the cookies to cool completely before frosting.

To prepare the frosting, beat the cream cheese, softened butter, and brown sugar in a bowl until smooth.

Gradually stir in the powdered sugar until the frosting is thick but spreadable.

Frost the cooled cookies generously and finish with a light sprinkle of nutmeg or cinnamon if desired.