Preheat the oven to 425 degrees F (220 degrees C).
In a large bowl, cream together butter, shortening, brown sugar, and 1/2 cup white sugar until smooth. Beat in the egg, and stir in the vanilla. Combine the flour, cream of tartar, baking soda, and salt; beat into the creamed mixture.
Roll dough into 1 inch balls. Dip the top half of the balls into water, then into remaining white sugar. Place sugar side up onto ungreased cookie sheets. Flatten slightly.
Bake for 8 to 10 minutes in preheated oven, or until light brown. Cool on wire racks, and store in an airtight container.