In a medium bowl, whisk together the gluten-free all-purpose flour, pumpkin pie spices, baking powder, baking soda, and salt. Set aside.
Using a stand mixer fitted with the paddle attachment or a hand mixer, beat the softened butter, brown sugar, and granulated sugar on medium-high speed for 3–5 minutes, until light and fluffy.
Add the pumpkin puree, egg, and vanilla extract and mix until combined.
Gradually add the dry ingredients and mix on low speed until combined. Avoid overmixing, which can make the cookies less tender.
Add the gluten-free rolled oats and gently fold them into the dough with a rubber spatula.
Cover the dough and refrigerate for 1 hour.
Preheat the oven to 350°F (180°C). Line 2 baking sheets with parchment paper or a silicone mat.
Let the chilled dough sit at room temperature for about 5minutes, then scoop it into balls and place them on the prepared baking sheets, leaving about 2 inches between each cookie.
Bake for about 15 minutes, or until the edges are set and lightly golden. The center should still look slightly soft.
Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.