Start by beating the softened unsalted butter and granulated sugar together in a large mixing bowl using an electric mixer. Beat on medium speed until the mixture is light and fluffy, about 3-4 minutes.
Add the pumpkin puree, egg, and vanilla extract to the creamed butter and sugar. Mix on low speed until everything is well combined.
In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed. Stop once the flour is just incorporated.
Cover the dough with plastic wrap and refrigerate for at least 1 hour.
Preheat oven to 350°F (175°C). Line baking sheets with parchment paper or silicone mats. Scoop tablespoon-sized portions of dough and roll into balls. Place on prepared baking sheet about 2 inches apart.
Bake for 12-15 minutes, until edges are set but centers remain soft.
Let cookies cool on baking sheet for 5 minutes, then transfer to a wire rack to cool completely. Sift powdered sugar over the tops before serving.