Preheat the oven to 350°F. Line a large baking sheet with parchment paper.
In the bowl of a stand mixer, beat together the sugar, brown sugar and butter for about 3 minutes.
Beat in the eggs, one at a time until thoroughly mixed in. Add in the vanilla extract and combine. Add in the pumpkin and thoroughly combine with the other wet ingredients.
In a separate, large bowl whisk together the flour, baking soda, 3 teaspoons of the cinnamon, ginger, allspice, nutmeg, salt and baking powder.
Add the dry ingredients to the wet mixture in two or three additions until everything is just combined.
Drop the dough onto the prepared baking sheet using a 1-1/2 tablespoon scoop, spacing them about 2 inches apart.
Bake the cookies for 18 minutes until they are baked all the way through. Remove the cookies to a cooling rack to cool thoroughly.
In a small bowl whisk together the confectioner's sugar and remaining 1/2 teaspoon of cinnamon. Stir in the milk until it creates a slightly thick glaze. Spread the top of each cookie with the frosting (or you can also dip the tops into the glaze and gently shake off the excess) and place them on a cooling rack until the frosting sets - about 1 hour. Serve them up, or store the cookies in a sealed contained for up to three days.