Preheat the oven to 350 degrees. Line baking sheet with parchment paper.

Using a stand mixer or hand mixer, cream together butter and sugar until smooth.

Add in lemon zest and lemon juice, and mix until blended.

In a medium size mixing bowl, combine flour and cornstarch.

Gradually add dry ingredients in to batter and mix on low to medium speed, until well combined.

Chill dough for 30 min.

Once dough has been chilled, place a piece of parchment paper on a flat surface and add a small amount of flour to the parchment paper.  Lightly flour a rolling pin as well.  

Place half of the dough on the floured parchment paper and roll smooth to a ¼ of in thick.

Using a cookie cutter of your choice, cut out cookies and place them on the lined baking sheet.

Bake for 8-10 min. Remove from the oven and allow to cool on a cooling rack.

While cookies are cooling, add powdered sugar, corn syrup and lemon juice into a medium size mixing bowl and mix until blended.

Add milk a little at a time until desired consistency is reached.

Drizzle glaze onto the cooled cookies with a spoon.

Allow glaze to harden for 2 hours, then serve.