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. Use your fingers to rub the zest into the sugar, until the sugar has a sandy texture.

Add the butter and salt to the lemon-sugar mixture. Mix on medium speed with the paddle attachment until the mixture is smooth and creamy, about 2 minutes.

Stop the mixer, scrape down the bowl, add the egg yolk and lemon juice and mix on medium speed just until the ingredients are incorporated.

Add all the flour and mix it 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 come together and forms large clumps.

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 a parchment-lined cookie sheet or board. Prick each cookie in the center with a fork.

Chill the dough in the refrigerator for at least 20 minutes.

Preheat the oven to 300°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 cool them for 5 minutes on the cookie sheet before moving them to a wire rack to completely cool.

Store the cookies in an airtight container for up to two weeks.

To make the lemon glaze, 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.