In a medium bowl, whisk to combine the flour, baking soda, baking powder, cinnamon, pumpkin pie spice, and salt.
In the bowl of a stand mixer fitted with the paddle attachment (or an electric hand mixer), combine the butter, light brown and granulated sugars. Beat on medium speed for 2 to 3 minutes until well combined.
Add the egg and vanilla, then mix on low for 1 minute, until lightened in color and fluffy. Add the pumpkin and mix on low for about 30 seconds to combine. With a rubber spatula, scrape down the bottom and sides of the bowl and mix again until the ingredients are evenly distributed.
With the mixer on low speed, gradually add the flour mixture, mixing until just combined. Scrape the bowl down one last time and use a spatula to fold in any remaining flour. Cover and refrigerate for 30 minutes.
After the dough has been chilling for 15 minutes, preheat the oven to 350°F. Line two large baking sheets with parchment paper.
Use a 1½ tablespoon-sized triggered cookie scoop to portion the cookies to be about 1½-inches in diameter. Scoop the cookies directly onto the prepared pans, leaving about 2 inches of space in between each cookie.
Bake the cookies for about 11 minutes, until the edges are lightly golden and the centers are just set. Let cool on the sheet tray for 5 minutes before transferring to a wire rack to cool completely.
In a medium mixing bowl, sift the powdered sugar. Add the milk, melted butter, vanilla and and salt and whisk the mixture until it is completely smooth. Cover and set aside until ready to use.
Once the cookies are competely cool, drizzle or dip the tops of each in the icing.