Step 1Heat the oven to 350 degrees. In the bowl of a stand mixer using the paddle attachment, or in a large bowl using an electric mixer, cream together the shortening and sugar until light and fluffy. Add the eggs, one at a time, beating thoroughly between each addition.
Step 2In a separate bowl, sift together the flour, cream of tartar, baking soda and salt. Add to the shortening mixture, beating well. Gather the dough in a ball, wrap in plastic wrap and refrigerate until firm, about 30 minutes.
Step 3Tear off walnut-size pieces of dough and roll each into a ball. Dust with cinnamon sugar and place on an ungreased baking sheet, spacing the cookies about 2 inches apart. Bake until the cookies are light brown and firm on top, 10 to 15 minutes; the tops will be deeply cracked, and the centers will still be somewhat soft.
Step 4Cool the cookies on the baking sheet for 5 minutes, then transfer to a cooling rack to finish. Store in an airtight container.