Preheat oven to 350 degrees F and line 2 baking sheets with parchment paper.
In a stand mixer, or with an electric hand mixer, cream together the butter and granulated sugar on medium/high speed for about 3 minutes, until fluffy.
Add in egg, vanilla, and 1 TBSP lemon zest and beat until combined.
In a separate bowl, whisk together flour, xanthan gum, baking soda, and salt.
Slowly add the flour mixture to the butter on low speed. Once all of the flour mixture is added, increase speed to medium/high and beat until combined.
Using a cookie scoop, or a 1 TBSP measure, roll tablespoonfuls of dough into balls and place on cookie sheet 2 inches apart.
Bake, 1 cookie sheet at a time, for 15 to 17 minutes.
Remove from oven and let the cookies cool on pan for 5 minutes and then place cookies on a cooling rack to cool completely.
While cookies are cooling, make the glaze. Whisk together the confectioners' sugar, 1 TSP lemon zest, and about 2 TBSP of lemon juice. If glaze is too thick to spread on cookies, add another TBSP of lemon juice.
Spread glaze over all the cookies and allow cookies to set for about 20 to 30 minutes. Enjoy!
