In a large mixing bowl, cream together shortening, butter, granulated sugar, and brown sugar until light and fluffy. Add egg and beat to combine.
Add flour, cinnamon, cloves, nutmeg, allspice, baking soda and salt. Stir to combine. Divide dough in half.
Place half of dough onto a sheet of parchment or waxed paper. Roll into a log about 2 inches in diameter.
Repeat with the other half of the dough. Wrap both rolls in the parchment paper and refrigerate overnight. Dough can also be frozen at this point for up to 1 month.
When ready to bake, preheat oven to 350ºF. Cut dough rolls into ¼ inch slices and place 2 inches apart on parchment paper lined baking sheets.
Bake for 10 minutes or until just golden brown..
Cool for 2 to 3 minutes on baking sheet before removing to a wire rack to cool completely. Store in airtight container.
Notes
To keep cookies round, put the dough logs into two glasses, on their sides, open end to open end, in the refrigerator. This will keep the dough from flattening on one side as it chills. Or if you happen to have a couple of empty paper towel tubes, they work great, too.
If you want smaller cookies, make your logs longer and thinner.
Traditional windmill cookies have sliced almonds. I leave them out of my cookies because of nut allergies.