Preheat oven to 165 degrees C.
Combine softened butter, granulated sugar, and salt in the bowl of a stand mixer or in a large mixing bowl.
Mix until thick and creamy, about one minute. Use high speed with a handheld mixer and medium-high speed on a stand mixer.
Stop the mixer and scrape the bottom and sides of the bowl. Add the vanilla extract. Mix for an additional minute. Add the gluten-free flour.
Mix for about two minutes on medium-high speed. Be sure to use the flat paddle attachment.
Roll dough into a log and chill 20 minutes. Use a sharp knife and cut into rounds, about ¼-inch thick. Place the cookies onto a parchment-lined baking sheet, about 1 inch apart. Prick each cookie with a fork. Bake until the cookies are set, about 25 minutes. Look for the edges to be lightly golden brown.
Transfer individual cookies to a wire rack
Store cookies in an airtight container for up to one week. Or freeze the cooled cookies for up to two months in a freezer container.