In a medium bowl, whisk together gluten-free flour, baking powder, and salt.
In a large bowl, beat butter and sugar together until light and fluffy, about 3 minutes. Add egg, vanilla extract, and almond extract and beat until well combined.
Gradually add the flour mixture to the butter mixture, mixing on low speed until dough comes together. Divide dough in half and flatten each half into a disk.
Wrap each disk tightly in plastic wrap and refrigerate for at least 2 hours or up to overnight.
Preheat oven to 350°F and line baking sheets with parchment paper.
Working with one disk at a time, roll dough out on a surface lightly dusted with gluten-free flour to 1/4-inch thickness. Cut out shapes with cookie cutters and transfer to prepared baking sheets.
Bake for 8-10 minutes until edges are just set but not browned. The centers should look slightly underdone.
Cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely before decorating.