Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper. In a medium bowl, whisk together the gluten-free flour, baking powder, and salt.
In a large mixing bowl, cream together the softened butter and sugar until light and fluffy, using a hand mixer or stand mixer. Beat in the egg and vanilla extract until well combined.
Gradually add dry ingredients to wet ones, mixing until a dough forms. If dough is too crumbly, add a little milk until it’s manageable.Transfer dough to a sheet of plastic wrap. Wrap tightly and refrigerate for at least 1 hour.
Use your favorite Christmas cookie cutters to cut out shapes from the dough. Carefully transfer the cut-out cookies to the prepared baking sheet, leaving some space between each cookie.
Bake cookies in the preheated oven for 8-10 minutes, or until the edges are lightly golden. Be careful not to overbake. Remove from the oven and let them cool on the baking sheet for 5 minutes, then transfer the cookies to a wire rack to cool completely.
In a medium bowl, whisk together powdered sugar, milk, and vanilla extract until smooth and creamy. If you want to make different colors of icing, divide the icing into separate bowls and add food coloring to each bowl.
Once cookies are cool, use a small spatula or a pastry bag to ice the cookies with the prepared icing. Add sprinkles or edible glitter on top of the icing, if desired.Allow the icing to set for a few hours or overnight until it hardens.