Preheat oven to 350 degrees.

Combine butter and sugars in a medium bowl. Using an electric mixer, beat at medium speed, scraping bowl often, until light and fluffy. Add egg and vanilla; continue beating until well mixed. Mix in cream of tartar, baking soda and salt. Gradually mix in flour

Shape dough into 1 1/2 inch balls. Place 2 inches apart onto cookie sheets. Flatten to about 1 1/2 inches with bottom of glass (if the glass sticks, dip it in sugar first).

Bake for 7-9 minutes or until edges of cookies are lightly browned. Do not over-bake. Let cookies stand for 2-3 minutes on cookie sheet before removing to a cooling rack. Cool completely.

To make frosting, combine butter and cream cheese until smooth. Stir in vanilla extract and salt. Add powdered sugar in 1-2 cup increments until combined, then add milk one tablespoon at a time until frosting is desired spreading consistency. You may not use all the milk.