Preheat oven to 350 degrees. In a mixing bowl whisk together flour, cornstarch, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger for 20 seconds, set aside.
In the bowl of an electric stand mixer fitted with the paddle attachment, cream together butter, shortening and sugar until pale and fluffy.
Mix in egg yolks one at a time. Mix in pumpkin puree and vanilla extract. With mixer set on low speed, slowly add in dry ingredients and mix until combined.
Scoop dough out and shape into 3 Tbsp balls (I just filled 1/4 cup 3/4 full). Place on Silpat or parchment paper lined baking sheets (you'll only be able to fit about 8 per sheet, these are fairly large cookies), and using your fingers lying flat, evenly flatten cookies into rounds until they are slightly under 1/2-inch thick.
Bake in preheated oven 11 - 12 minutes. Cool on baking sheet several minutes then transfer to a wire rack to cool completely. Once cool frost with Cinnamon Cream Cheese Frosting. Store in an airtight container.
For the frosting:
In the bowl of an electric stand mixer fitted with the paddle attachment, whip together cream cheese and butter until pale and fluffy.
Mix in cinnamon, vanilla extract and powdered sugar. Mix in enough milk to reach desired consistency and mix until smooth and slightly fluffy.