In a large bowl, cream together the softened unsalted butter and white sugar until the mixture becomes very light and fluffy, about 3 minutes. This step is important for a tender cookie texture.
Add the room temperature egg, milk, vanilla extract, and salt to the butter and sugar mixture. Beat until the mixture is very well combined. The mixture may look separated at first, but continue beating until it comes together smoothly.
Gradually add the gluten-free all-purpose flour to the wet mixture and beat at low speed until just combined. Cover the bowl with plastic wrap and refrigerate the dough for at least 1 hour (or freeze for 30 minutes) until thoroughly cold.
Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper, or leave them ungreased if preferred, and set aside.
Sprinkle a little gluten-free flour onto your rolling surface or silicone mat. Take half of the cold dough (from Step 3) and roll it out to about 1/4" thickness. If the dough is too stiff, let it sit at room temperature for 5-10 minutes to become more pliable. Cut out shapes with cookie cutters and transfer to the prepared baking sheets using a spatula. Repeat with remaining dough. I like to chill the cookie trays in the fridge before baking, which helps the cookies keep their shape.
Bake the cookies for 10-12 minutes, or until the cookies are set. Let them cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely before decorating. I always wait until the cookies are fully cool before icing, to prevent the decorations from melting.