Cream the butter and sugar together well, then add in your eggs. Beat until fully incorporated, then add in the vanilla.
Zest an entire lemon into the dough, then mix in.
In another bowl, whisk together your dry ingredients.
Mix together in a bowl. The key here is to not use a mixer as it will make the dough fluffy. Work those arm muscles and incorporate all of the flour into the dough.
Form into a ball and place in a plastic sealed bag. Refrigerate for an hour.
A handy tip for cutting out sugar cookies is to roll the dough onto your parchment paper about 1/4 to 1/2 inch thick, cut out your shapes, then remove the excess dough, leaving the shapes untouched and unmoved on the parchment, then just lift and place onto a baking sheet. Easy!
Bake in a 350 degree oven until the edges just barely start to get brown, about 6-8 minutes.
Remove and cool completely on the sheets.
For the icing, whisk together all of the ingredients.
In order to get thinner icing I added a little more milk until I could dip my cookies into the icing, and let them drip off, getting this beautiful glazed coating below. Do NOT put in more corn syrup, it will never harden and set properly. So add milk very little by little until you get the consistency you need.