Preheat the oven to 350°F (175°C) and line two large baking sheets with parchment paper or silicone mats.
In a small bowl, combine the pumpkin puree and baking soda; stir well and set aside for 5 minutes to allow the chemical aeration process to occur.
In a large mixing bowl, cream the softened butter with the granulated sugar and brown sugar using a stand mixer or hand mixer until the mixture is light and fluffy.
Incorporate the egg and vanilla extract into the butter mixture, beating until well combined.
Fold the pumpkin and baking soda mixture into the wet ingredients.
In a separate medium bowl, whisk together the gluten-free flour, salt, pumpkin pie spice, and cinnamon.
Gradually add the dry ingredients to the wet mixture, mixing on low speed until a consistent dough forms.
Drop rounded tablespoons of dough onto the prepared baking sheets, spaced approximately 2 inches apart.
Bake for 10 to 12 minutes or until the edges are set and the tops feel slightly springy to the touch.
Allow the cookies to cool on the baking sheet for 10 minutes to stabilize the structure before transferring them to a wire cooling rack.