Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together the gluten-free flour blend, baking powder, and salt. Set aside.
In a large bowl, using an electric mixer, beat the softened butter and granulated sugar together on medium speed until light and fluffy, about 2 to 3 minutes.
Add the egg and vanilla extract to the butter mixture and beat until fully combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.
Add the milk and mix until the dough comes together and is smooth. If the dough is too sticky, add a little more gluten-free flour, one tablespoon at a time.
Using a tablespoon or cookie scoop, scoop dough and roll into balls. Place them about 2 inches apart on the prepared baking sheets.
Flatten each ball gently with the bottom of a glass or your hand to about 1/4 inch thickness.
Bake in the preheated oven for 9 to 11 minutes, or until the edges are set and just beginning to turn golden.
Remove from the oven and allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.