Preheat the oven to 400°F. Lightly grease (or line with parchment) two baking sheets.   To make the dough: Beat together the shortening (or butter) and sugar till smooth, then add the eggs, again beating till smooth. Beat in the vanilla, cream of tartar, baking soda (or baking powder, in place of the cream of tartar and soda), and salt, then add the flour, mixing slowly till combined. (If you beat the dickens out of the dough at this point, your cookies run the risk of being tough.) Place dough in the refridgerator for a couple of hours so it is easier to scoop and shape.   To shape the cookies: Drop the dough by teaspoonfuls (a teaspoon cookie scoop works wonderfully well here) on a lightly greased or parchment-lined cookie sheet, leaving about 1 ½" between them.   To bake: Bake the cookies for 10 to 11 minutes, reversing the position of the pans (top to bottom, and back to front) midway through. At the midway point, use the bottom of a glass (or the end of the pusher from your food processor) to flatten each cookie till it's about ¼" thick and 1 ½" in diameter. Then dust with a little cinnamon/sugar. Return to oven for 5 more minutes, until lightly golden brown.   Yield: about 50 cookies. Approx 2g sugar per cookie.