Preheat oven to 350F. Sift the flour, baking soda, baking powder, salt and spices into a large bowl. Whisk together and set aside.
Cream the butter, and sugars together in a stand mixer fitted with a paddle attachment (or using an electric mixer). Beat until lighter in color and fluffy.
Add the egg and vanilla while mixing on low, then mix in the pumpkin. Scrape the bowl down and mix again until ingredients are distributed.
Add the flour mixture in then mix on low to medium-low until just combined. Scrape bowl down one last time and use a spatula to fold in any remaining flour. Cover and chill for at least 30 minutes, preferably an hour or two.
Use a triggered ice cream scoop or tablespoon to potion out 1.5-2 inch balls. Roll each into a ball with your clean palms for a more rounded cookie.
Place balls about two inches apart on a parchment paper or silicon-lined baking sheet and bake at 350F for about 11 minutes. The cookies' edges will be set but the centers appear baked.
While the cookies are cooling you can mix the icing. Add the powdered sugar to a bowl then drizzle in the vanilla and milk. Mix until smooth and add more milk if needed to get a drizzling consistency.
Arrange the cookies close together and drizzle icing over the top. You can use a spoon or pipe it out from a piping bag.