Preheat oven to 325°F (163°C). Line a baking sheet with parchment paper.
In a large bowl, beat the butter with an electric mixer until smooth and creamy.
Add the powdered sugar, vanilla extract, and salt. Mix until fully combined.
Gradually add half the gluten-free flour, mixing until blended. Then add the remaining flour and mix until a soft, crumbly dough forms.
Bring the dough together into a ball with a spatula or your hands.
On a lightly floured surface, roll out the dough to just over 1/4-inch thickness. Cut into shapes using a 2 1/4-inch cookie cutter.
Transfer cookies to the prepared baking sheet, spacing them about 1-inch apart. Pierce each cookie with a fork.
Bake for 15 minutes, or until lightly golden.