In a large mixing bowl, beat the butter, shortening, and sugars until fluffy. Add egg and vanilla and mix until well blended. Mix in flour, baking soda, cream of tartar, and salt just until blended.
Roll dough into balls. Dip half into water, then into sugar. Place sugar-side up on an ungreased baking sheet.
Bake at 400 degrees F for 6 to 8 minutes. Cookies will be puffy. Let cool on baking sheets for at least 5 minutes before removing to wire racks to cool completely. Store in an airtight container.