Preheat oven to 425 F/218 C. Prepare baking sheets by greasing, or covering with parchment or a silicone mat.
Make the frosting: Combine butter, cream cheese, vanilla, milk, and salt. Mix in powdered sugar one cup at a time, until fluffy and smooth. Set aside.
Make the sour milk and set aside. Cream the butter and sugar very well. Add in the eggs, and beat until light and fluffy. Beat in sour cream, sour milk, vanilla, and salt. Mix in one cup of flour at a time. Dough will be sticky and thick, similar to brownie batter.
Drop tablespoons of dough onto prepared cookie sheet, and bake for 5-7 minutes until just done. Cookies will puff up and spread quite a bit. They do not get brown on top.