In a medium bowl, cream butter and sugar. Add the vanilla and mix until well combined. Combine the flour, cornstarch, and salt. Cream the flour mixture with the butter and sugar, mixing well. Stir in the milk and the pistachios, mixing until a ball is formed.
Remove the dough from the bowl, wrap in plastic wrap, and chill for an hour.
Once chilled, form into 24 balls, approximately a half of a tablespoon of dough. Place on an ungreased baking sheet and press down with your thumb to form an indent for the frosting, flattening a couple times. From here, preheat the oven to 350 degrees (325 on convect) and chill the cookies one more time while the oven preheats.
Bake for 12-15 minutes, until the cookies are just starting to brown. Shortbread is easy to over bake so watch them carefully. Once done, remove and allow to cool.
Meanwhile, make the frosting. Cream the butter and vanilla. Stir in the powdered sugar and a pinch of salt. Add the lime juice and cream until a smooth frosting is formed. Give it a taste test. If it is too tart, add a bit more sugar. If it is too thick, add a splash of milk (a tablespoon or so).
Put into a piping bag and pipe the frosting into the center of each cookie. Sprinkle with remaining ground pistachios. Allow the frosting to harden before packaging in an airtight container.