Step 1

For the cookies: In a medium bowl, whisk together the flour, pumpkin pie spice, baking soda, and salt. Set aside.

Step 2

In the bowl of a stand mixer fitted with a paddle attachment, beat the sugar and butter on medium speed until light and fluffy, about 3 minutes. Beat in the pumpkin puree, egg, and vanilla extract until well combined, about 1 minute. Add the flour mixture and beat on low speed just until the dry ingredients are incorporated, about 30 seconds. Cover and chill the dough for at least 2 hours or up to 2 days.

Step 3

Preheat the oven to 350°F. Line two cookie sheets with parchment paper.

Step 4

Scoop the dough into balls, about 2 tablespoons each, and arrange the dough balls at least 2 inches apart on the prepared baking sheets.

Step 5

Bake until the cookies are puffed and lightly browned around the edges, 11 to 12 minutes. Let the cookies cool on the baking sheets for 3 minutes. (The cookies will collapse slightly as they cool.) Transfer to a wire rack to cool completely, about 30 minutes.

Step 6

For the icing: In a medium bowl, whisk the powdered sugar, pumpkin puree, pumpkin pie spice, and water until fully combined. Spoon about 1 teaspoon of the icing on the top of each cookie and spread to cover the top. Sprinkle the cookie with white sparkling sugar, if you like. Let the cookies sit for about 45 minutes, or until the icing has hardened.