Preheat the oven to 375° F. Line a cookie sheet with parchment paper or a silicone baking mat.
In the bowl of a stand mixer or with an electric hand mixer combine the partially melted butter and brown sugar until combined.
Add the egg, pumpkin puree and vanilla, mixing well.
Add the flour, cornstarch, cinnamon, soda and salt to the bowl. Slowly start mixing. As the dry ingredients are mixing in, slowly add in the buttermilk.
Mix until a thick batter forms.
Scoop the batter onto the pan using a #40 scoop (1 1/2 tbsp) for small cookies or a #24 scoop (3 tbsp) for larger cookies.
Bake at 375° F for 8-12 minutes or until the cookies have spread and no longer look wet and underbaked in the center of the cookie.
Allow the cookies to cool on the pan.
While the cookies are cooling, make the frosting.
In the bowl of a stand mixer, cream together the softened butter and cream cheese until mixed thoroughly.
Scrape the sides of the bowl and then alternate adding the remaining filling ingredients, adding a portion of the powdered sugar and then some liquid, letting the mixer go on low until the powdered sugar is completely incorporated before adding more.
Repeat this process until all of the ingredients have been added. You can adjust the consistency of the frosting by adding more heavy cream to this the frosting or more powdered sugar to thicken the frosting.
Spread the frosting onto each cookie. Garnish with some cinnamon sugar, if desired.
Store in an airtight container for up to 3 days.
Enjoy!