In a large mixing bowl (or stand mixer), cream together butter, Crisco, sugar, powdered sugar and milk.
Add eggs and mix until well combined. In a separate bowl, combine flour, baking soda, cream of tartar and salt.
Add the flour mixture to the butter mixture and mix until smooth and well combined.
Roll the dough into 1-inch balls and place on a greased cookie sheet.
Spray the bottom of a glass or measuring cup with cooking spray and then dip into a plate coated with a thin layer of sugar. Press each ball down slightly to get the rough edge that Swig cookies are known for. You don't want to smash them too thin because these cookies are best when they are thick and soft.
Bake for 8-9 minutes at 350. Cool on wire racks and then frost.
To make the frosting, mix all of the ingredients except for the milk until well combined. Add milk to desired consistency and then frost the cooled cookies.