Heat oven to 350 F. Line a cookie sheet with a sheet of parchment paper.

In a large bowl, combine the powdered sugar and butter and beat well with an electric mixer on medium speed. Add the milk and egg yolk and beat until completely combined, scraping down the sides of the bowl.

Add flour and cornstarch to the wet ingredients and mix well. (If using a stand mixer, switch to dough hook. Otherwise, you will need to stir by hand with a sturdy spoon; this is a very thick dough.)

Stir or knead in the cashew pieces.

Using 1 tablespoon of cookie dough at a time, roll dough into balls. Place dough balls on prepared baking sheet, 1 ½ inches apart. Firmly press the top of each cookie with your thumb (or a round spoon handle or melon baller). Repair any large cracks around the edge of the cookie.

Bake 9 - 11 minutes, or until the cookie bottoms are lightly golden brown. Transfer cookies to a wire rack to cool completely.

In a medium pan, combine the brown sugar, butter, and milk. On medium heat, bring mixture to a boil, stirring often. Once boiling, cook for 2 minutes.

Remove from heat. Whisk in the vanilla and powdered sugar until mixture is smooth.

Carefully spoon the caramel into the depressions on cookies. The caramel sets quickly, so If you are adding cashews on top, pour 4 cookies at a time and add the cashews. Repeat until all cookies are filled. If the icing gets too thick to pour, place it back on the stove at low heat briefly, stirring constantly.