In a small bowl, whisk together the flour, corn starch and salt, then set aside.
In the bowl of an electric mixer, beat butter until smooth. Add powdered sugar, and beat until fully incorporated.
Add lemon zest, then, while mixing, slowly add lemon juice.
While mixing (on low), slowly add flour mixture and blend until all of the flour is fully incorporated.
Stop mixing and scrape down the sides of the bowl, then cover and refrigerate dough 30 minutes to 1 hour.
When the dough has chilled, use a 1 tablespoon sized scoop to scoop out dough, then roll dough into balls and place on a parchment paper lined, or Silpat lined baking sheet. Press down on the dough balls just a bit to flatten the tops. Place entire baking sheet (with cookie balls) in the fridge or freezer while the oven heats up.
Bake in preheated oven at 350°F. for 11-13 minutes, or just until the edges of the cookies are golden brown.
Cool just a bit on the baking sheet, then move cookies to a wire cooling rack.
When cookies have been baked and cooled, make glaze.
To make glaze, simply whisk together powdered sugar, lemon zest and 2 tablespoons lemon juice. Add a bit more lemon juice as needed to reach desired consistency.
Dip cooled cookies into glaze, then return to wire cooling rack (with a baking sheet below to catch excess glaze) and allow glaze to set up before storing cookies.