Whisk together gluten-free flour, baking powder, and salt in a medium bowl.
In a large bowl or stand mixer, cream together the softened butter and granulated sugar until light and fluffy.
Add the egg, vanilla extract, and almond extract; beat until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until a dough forms.
Wrap the dough in plastic wrap and refrigerate for at least 30 minutes to improve texture and prevent spreading.
Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.
Scoop 1.5 tablespoon portions of dough, roll into balls, and place 2 inches apart on the prepared sheets.
Lightly flatten each ball with the bottom of a glass dipped in sugar.
Bake for 9 to 11 minutes or until the edges are just set but not browned.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack.