In a large bowl combine the sugar and lemon zest. Rub sugar and zest together with your fingertips. ½ cup (100 g) granulated sugar 2 tablespoons lemon zest
In a bowl of stand mixer, fitted with a paddle attachment (or you can use a hand mixer), on medium speed cream together the butter, sugar and lemon zest until light and fluffy, about 2 minutes. With a rubber spatula or wooden spoon, scrape down bowl as needed. 1 cup (2 sticks, 225 g) unsalted butter
Add in vanilla and lemon juice beat to combine. 2 teaspoons vanilla extract 2 tablespoons lemon juice
Add flour and salt, and beat on low speed until the dough comes together. 1 teaspoon fine sea salt 2 ¼ cups (270 g) all purpose flour
Dump your dough out onto a lightly floured surface and shape into a disc. Wrap in plastic wrap and chill for 15 minutes before rolling out and cutting.
Position a rack in the center of your oven. Preheat oven to 350°F. Line a baking sheet with parchment paper.
On a lightly floured surface, with a lightly floured rolling pin, roll out dough to a ¼”-½” thick using a rolling pin. Be sure to rotate the dough after every few rolls, to ensure the dough isn’t sticking. If the dough cracks, simply press it back together. Using a cookie cutter of choice, cut out your cookies. Press scraps back together and re-roll (if dough is getting to warm or sticky, pop back into the fridge). Keep in mind the more your re-roll the scraps the dough will get tougher.
Place cookies onto baking sheet, spaced about 2 inches apart. Bake in preheated oven for about 12-15 minutes. Remove from the oven and allow to cool on the cookie sheet for 5 minutes. Transfer to a wire rack to continue cooling.
Make icing. In a small bowl whisk together powdered sugar and lemon juice. Spread on each cookie. ¾ cup (85 g) powdered sugar 1-2 tablespoons lemon juice