Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or silicone baking mats.
In a medium bowl, whisk together the gluten-free flour, baking powder, baking soda, and salt. Set aside.
In a large mixing bowl, cream the softened butter, granulated sugar, and powdered sugar together until light and fluffy, about 2-3 minutes.
Beat in the egg, vanilla extract, and almond extract until well combined.
Gradually add the dry ingredients to the wet mixture, mixing until just combined. Do not overmix.
Scoop out about 2 tablespoons of dough and roll into a ball. Place the dough balls onto the prepared baking sheets, spacing them about 2 inches apart. Lightly press down on each ball to slightly flatten.
Bake in the preheated oven for 10-12 minutes, or until the edges are set and the cookies are lightly golden. They will look slightly underbaked in the center, which is okay. Let them cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.
In a medium bowl, beat the softened butter until creamy. Gradually add the powdered sugar, 1/2 cup at a time, beating until combined. Add the heavy cream (or milk) and vanilla extract, and continue to beat until the frosting is smooth and fluffy. If desired, add a few drops of food coloring and mix until evenly colored.
Once the cookies are completely cooled, spread a generous amount of frosting on top of each cookie. Add sprinkles, if desired.