Prepare the frosting so it will be warm to frost the cookies but not so hot it runs off.
First, sift the powdered sugar well and set it aside. In a small non-stick pot, melt the butter.
Whisk in the brown sugar and bring to a boil. Boil for 2 minutes.
Carefully whisk in the vanilla and sweetened condensed milk.
In a mixing bowl, cream the butter and the sugars. Mix in the egg yolks, vanilla, and salt. Stir in the flour, mixing well.
Whisk in the sifted powdered sugar a ¼ cup at a time. It is important that the powdered sugar be sifted to avoid lumps.
Remove from the hotter heat, but keep the frosting warm by either putting it in a non-stick pot on the stovetop over very low heat in between frosting batches or putting it in a chocolate melting pot set on low. Make the cookies.
Preheat the oven to 375 degrees. Spray baking sheets with non-stick cooking spray or line them with parchment paper. In a mixing bowl, cream the butter and the sugars.
Add the egg yolks and the vanilla. Mix well.
Add the salt and the flour. Mix well.
Scoop out the dough by ½ tablespoonfuls and roll into balls. Each ball should be the size of a gumball.
Place on prepared baking sheets. I was able to cook 20 cookies per pan.
Flatten each cookie with a fork in a crisscross pattern.
Bake at 375 degrees for 8 minutes. These cookies won't brown until they are overdone, so don't wait for them to brown, or they will be crispy.
Cool the cookies on a cooling rack.
While the cookies are still a little warm but not hot, frost them with the warm caramel frosting.
Allow the frosting to cool and set.
Store in an airtight container with wax paper separating the layers of cookies.