Preheat the oven to 300℉, and line two baking sheet with parchment paper. Set them aside.
Use your clean fingertips to rub the lemon zest and sugar until the oil and aroma are released from the lemon zest. Set this aside.
½ cup Granulated sugar, 1 tablespoon Lemon zest
Cut the cold butter into thin slices. Beat the butter, vanilla extract, and sugar-lemon zest mixture using the paddle attachment. Keep the mixture at a low speed. We do not blend the butter fully.
1 cup Butter, ½ teaspoon Vanilla extract
Remove the mixture from the mixer, and add the flour and salt. Use your fingertips to incorporate the flour into the butter mixture for a couple of minutes until the mixture forms large crumbs.
2¼ cup All-purpose flour, ½ teaspoon Salt
Gather the dough into a large ball. Lightly flour a working surface and roll the dough to ½ inch thickness. Use an egg shape cookie cutter or any desired cutter to cut the cookies. Place the cookies on the lined baking sheets, and bake them for 20 to 25 minutes or until the edges turn light brown.
How To Make The Glaze
Add a couple of tablespoons of lemon juice to the powdered sugar and mix well. If the mixture is too dry, add another tablespoon of lemon juice; if it is too runny, add a small amount of powdered sugar. The mixture should have the consistency of warm honey.
1 cup Powdered sugar, 3-4 tablespoon Lemon juice
Brush the glaze on the warm cookies and let the glaze set for half an hour.