Combine the flour, sugar, and lemon zest in a large bowl.
Add in the chilled butter and cut it into the flour with a pastry cutter, it will look like coarse crumbs.
Then add in the egg yolk with a fork till it’s fairly well blended. Because my dough was so dry and would not knead together I had to had 4 tablespoons of ice water to the dough before I could form a ball and have it come together well. I did this a half tablespoon at a time.
Cut the dough ball into half and roll each half into a log of about 1 inch diameter and then wrap them in plastic wrap. Place in the freezer (NOT THE FRIDGE) for about 30 minutes.
Once chilling is done preheat oven to 350 and remove logs and slice into 1/4 inch rounds with a serrated knife. Place on baking sheet with paper (I skipped the paper they turned out fine) for about 10-12 minutes. Allow them to cool before glazing.
To make the icing we squeezed lemon juice out of the lemons we grated. Mix 3 tablespoons of fresh lemon juice with 1 cup of powdered sugar, till well mixed. I used a spoon to drizzle over the cookies or you can use a piping bag.