Preheat the oven to 350F. Line a baking sheet with parchment paper.
In a large bowl, combine sugar and spices; remove 1/2 cup of this mixture and place in a medium-sized, shallow dish or bowl (like a soup plate). Add butter to bowl and cream with sugar mixture until fluffy. Beat in eggs, one at a time, and vanilla extract.
In a medium bowl, whisk together flour, salt, cream of tartar and baking soda. Add to sugar mixture and stir until fully incorporated.
Shape dough into 1 inch balls and roll in reserved sugar-spice mixture. Place on baking sheet, leaving 2 inches between balls to allow for spreading.
Bake for about 12 minutes, until edges are firm to the touch, but not quite browned. Cool for 3-5 minutes on the baking sheet, then transfer cookies to a wire rack to cool completely.
Makes about 4 dozen.