In a large mixing bowl (or stand mixer), cream together butter, shortening, 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°F. Cool completely on wire racks.
To make the frosting: Mix the butter, sour cream, powdered sugar and vanilla together with an electric mixer until well combined. Add the milk, just a little bit at a time to get a spreadable consistency. Separate out about two ½ cup portions of the frosting and use food coloring to dye one red and the other green.
To pipe a rosette, transfer frosting to a piping bag fitted with an open star tip. The size depends on you and what you're frosting! You can't go wrong with the classic 1M tip.
To achieve the swirled color look, lay out two 14" long sections of plastic wrap. Put about 1 cup of white frosting down the center of each in about a 6-7" line. Then take the red frosting and layer it on one of the segments of white frosting. Put the green frosting on the other piece. Take the long edges of the plastic wrap and fold them over to seal the frosting in a tube of plastic wrap. Then transfer the tube to a piping bag fitted with a 1M star tip. Pull the plastic wrap down into the bag and through the tip. Snip the plastic wrap nearest the piping tip and use your hands to move the frosting down, to where it can be piped.
Pipe a small star in the center of a cookie and continue piping directly around the star, continuing until the edge of the cookie. Alternate colors as you'd like and feel free to top with Christmas sprinkles, if you prefer. Enjoy!