Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together the gluten free all-purpose flour, baking soda, and salt. Set aside.
In a large bowl, using an electric mixer, beat the softened butter and granulated sugar together on medium speed until creamy and smooth, about 2 minutes.
Add the brown sugar to the butter mixture and beat until combined.
Beat in the egg and vanilla extract until fully incorporated.
Gradually add the dry flour mixture to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Using a tablespoon or cookie scoop, drop rounded balls of dough about 2 inches apart onto the prepared baking sheets.
Bake in the preheated oven for 9 to 11 minutes, or until the edges are lightly golden but the centers remain soft.
Remove from the oven and allow the cookies to cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.