Preheat oven to 350°F (180°C). Line 2 to 3 baking sheets with parchment paper.

In a large bowl, whisk together brown sugar, melted butter, pumpkin, egg, and vanilla.

In a medium bowl, whisk together flour, pie spice, cinnamon, baking soda, salt, and espresso powder. Gradually add flour mixture to sugar mixture, stirring just until combined. Using a 3-tablespoon spring-loaded scoop, scoop dough into mounds (about 50 grams each), and place 2 inches apart on prepared pans.

Bake, one batch at a time, for 7 minutes, and rotate pan. Place a 3½- to 4-inch round cutter around hot cookies, one at a time, and gently move cutter in a circular motion while contacting edges of cookie until desired shape is reached. Bake until edges are set and tops are just set, 3 to 5 minutes more. Remove from pan, and let cool completely on wire racks.

Using a small offset spatula, spread Espresso Frosting on top of cooled cookies (about 18 grams each). (See PRO TIP.) Garnish with pie spice, if desired. Refrigerate in an airtight container for up to 2 days.