Place the sugar in the bowl of an electric stand mixer. Zest the lemons directly onto the sugar, until there is about three (3) teaspoons of zest.
Place the butter, sugar, and salt in the bowl of a stand mixer with the paddle attachment and mix on medium speed until the mixture is smooth, about 2 minutes.
Stop the mixer, scrape down the bowl, add the egg yolk and lemon juice and mix in on medium speed just until the ingredients are incorporated.
Add all the flour and mix it in on low speed just until all the flour is mixed in. The dough will be crumbly at this point. Increase the mixer speed to medium and mix until the dough has completely come together and forms a dough.
Turn the cookie dough out onto a lightly floured surface. You can also turn it out onto a large piece of parchment paper or Silpat. Use your hands to shape the dough into a rectangle and lightly flour the top of the dough. Do not use too much flour, just enough to keep the rolling pin from sticking.
Roll the dough out to ¼-inch thick. Use a 2-inch round cookie cutter to cut out the cookies. Place the cookies on parchment-lined cookie sheet or board. Prick each cookie in the center with a fork. Pricking the cookies will ensure that the steam releases as they bake and you'll end up with an even cookie.
Chill the dough in the refrigerator for at least 20 minutes. Chilling the dough will help the cookies hold their shape when baking.
Preheat the oven to 300 degrees F. Line a half baking sheet with parchment paper. Place the cookies on the baking sheet 1-½ inches apart.
Bake the cookies for 20-22 minutes. The bottom of the cookies will be lightly golden brown.
Take the cookies out of the oven and allow them to cool for about 5 minutes on the cookie sheet before moving them to a wire rack to completely cool.
At this point the cookies are ready to eat.
Store the cookies in an airtight container for up to two weeks.
The cookies are delicious on their own but this lemon glaze amps up the lemon flavor makes a nice presentation if serving the cookies at a party
Sift the powdered sugar into a medium-sized mixing bowl. Add 3 teaspoons of lemon juice and stir together. Add the remaining lemon juice ½ teaspoon at a time until the desired consistency is achieved.
Use an offset spatula or the back of a small spoon to spread the lemon glaze across the top of the cookie. Lay the cookies on a flat surface and let the glaze dry.
If serving the cookies right away and while the glaze is still wet make sure not to stack the cookies.
