In a large mixing bowl, combine the powdered sugar and lemon zest. Rub them together with your fingertips for 1 minute until the sugar is fragrant with lemon.
Add the unsalted butter and vanilla extract to the bowl. Whisk for 30 seconds until the mixture is well combined and smooth.
Incorporate the large egg and egg yolk into the mixture. Whisk for 1 minute until everything is smooth and fully blended.
Pour in the freshly squeezed lemon juice and whisk for 30 seconds until the mixture becomes smooth and uniform.
In a separate bowl, whisk together the gluten-free flour blend, xanthan gum, and baking powder. Gradually add these dry ingredients to the wet mixture in three additions.
Stir with a rubber spatula until a soft, batter-like dough forms. Avoid overmixing, stirring for no more than 1 minute.
Cover the dough and chill it in the refrigerator for at least 2 hours to firm up and prevent spreading during baking.
Preheat your oven to 350°F (180°C) and line 2 baking sheets with parchment paper, preparing them for the cookies.