Meanwhile, prepare the pumpkin cookie dough. Start by lining a plate with several layers of paper towel, then place the pumpkin puree on top. Press down with several more layers of paper towel to remove the excess moisture. Repeat until the pumpkin is dry and about half the volume. Set the dried pumpkin aside until needed.
In the bowl of a stand mixer fitted with the paddle attachment, add the butter, brown sugar and granulated sugar and beat together until smooth and fluffy, about 3-5 minutes. Add the dried pumpkin, egg, and vanilla extract and beat until smooth and well combined.