In a bowl, whisk together flour, sugar, salt, lemon zest. Add cold butter cubes to the bowl and work into the flour mixture with your fingers until it resembles coarse crumbs.
Make well in the center of bowl and add egg yolk, vanilla extract and combine with flour mixture. Add water gradually to bind the mixture. Knead gently and form dough in to a ball and wrap in plastic wrap. Chill in the fridge for 2-24 hours.
Preheat oven to 350° and line a baking sheet. On a lightly floured surface, roll out dough to ¼" thickness and use 2½" cookie cutter or mini tartlet mold (2½" across) to cut out cookies. If the dough is too hard, leave on the counter for 5-10 minutes before rolling it out. Arrange cookies at least 1" apart on a lined baking sheet and bake 10-12 minutes or until cookie edges are starting to turn light golden brown. Cool cookies for few minutes on the baking sheet then transfer to cooling rack and let cool completely.
In a small bowl, whisk together icing sugar, flour, lemon juice and milk. Brush glaze over each cookie and let cookies sit on a rack until glaze sets.