In the bowl of an electric mixer, cream together butter and sugar until light and fluffy.
Add egg, vanilla extract, and vanilla beans. Mix until combined.
In a separate bowl, combine flour, baking powder and salt. Add in increments to wet ingredients and mix until combined.
Chill dough in refrigerator for at least 1 hour.
Preheat oven to 350 degrees F. Roll dough into balls and flatten with the bottom of a glass. Use flour if dough is very sticky.
Bake for 9-11 minutes (do not over-bake). Remove from oven and allow to cool completely before glazing.
In the bowl of an electric mixer (or using a hand mixer), whisk the powdered sugar, light corn syrup, milk, and vanilla beans until smooth. If glaze is too thin, add more powdered sugar. If glaze is too thick, add more milk.
Spoon glaze over each cookie and allow to set.
Store cookies in an airtight container for up to one week.