Place two clean, ungreased aluminum sheet pans in the refrigerator to chill. Do not use parchment paper or silicone mats. Weigh or measure the brown sugar into a small bowl. In another bowl, whisk together the flour, baking powder, salt, and pumpkin pie spice.
Cream the room-temperature butter for 1 to 2 minutes until it forms soft peaks. Add the brown sugar and mix on medium speed for about 3 minutes.
Add the pumpkin puree and vanilla extract, mixing until combined. Add the egg and mix until incorporated. Scrape down the bowl. With the mixer on low, add the flour mixture about a third at a time, mixing until incorporated. The dough should feel like soft playdough and hold its shape. Do not chill the dough.
Choose your cookie press disk and assemble the press. Shape the dough into logs that fit inside the cylinder, filling it almost to the top. Attach the top and operate the lever until the dough begins coming through the disk.
Preheat the oven to 350°F (175°C or 180°C). Take one cold sheet pan from the refrigerator. Place the cookie press flat against the pan and press down gently. Push the lever down once, release it, and let it return to its starting position. Wait a second, then lift the press straight up without tilting the base. Space the cookies about 1 inch apart. Bake for 9 to 11 minutes, then transfer to a cooling rack.