Cream together butter and sugar until light and fluffy.  Add eggs, one at a time, and mix well after each addition.  Mix in vanilla.  In a separate bowl, combine flour, baking soda, cream of tartar and salt.  Add, one third at a time, to butter mixture, mixing until blended after each addition.  Refrigerate dough until chilled, or overnight.

Drop by rounded teaspoonfuls into coarse sugar and place on parchment lined cookie sheet.  (I used a 1" cookie scoop)

Bake at 375 degrees for 9 minutes, or until cookies appear set and very lightly golden on bottom.  Transfer to cooling rack.