Use an electric mixer to beat the butter, sugar, salt and vanilla until light and creamy. Add the egg and yolk; mix to fully incorporate. Add the flour, mixing until just combined. Remove dough from the mixer and wrap in plastic wrap. Flatten into a disc and refrigerate for at least 2 hours, preferably overnight.
Preheat oven to 375 degrees. Working with ¼ of the dough at a time, roll the dough on a lightly floured surface, to ¼ inch thick. Dough needs to be cold or it will get sticky and will not hold cookie shape.
Be sure to place on parchment paper, bake 11 minutes, remove from oven, wait 1 minute and move to cooling racks. Remove even if they don’t appear to be cooked or they will be hard and crunchy.
For the Glaze:
In a small bowl, whisk together the confectioners’ sugar, corn syrup, and 1 ½ tablespoons of the milk until smooth.
Add food coloring, if desired
Spread one cookie with glaze, using a table knife or offset spatula. If it doesn’t smooth out after 1 minute, dribble in additional milk, ½ teaspoon at a time, until the glaze reaches the right consistency.