Blend together the soft butter, sugar, cornstarch and flour until everything is well incorporated. Cover with plastic and chill for at least an hour.

Preheat oven to 350F

Using a small spoon or a scoop, form small heaps or balls of dough and set them on an ungreased, cookie sheet. You can use parchment paper if you like.

Bake for 12-15 minutes until the bottoms are just starting to turn a light brown. The tops will be white. Let the cookies cool a while on the baking sheet, and then transfer them carefully to a cooling rack. The cookies are very delicate, so use a very thin spatula to move them.

Let them cool completely before frosting.

Make the frosting by mixing the butter, sugar, vanilla, and enough milk or cream to make a spreadable consistency. It should be quite thick.

Dab it on top of the cooled cookies, and garnish with some grated chocolate.