Into a medium bowl, sift together the flour, ginger, cloves, nutmeg, and allspice; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat the shortening and sugar until light and fluffy.
Meanwhile, in glass measuring cup, combine the rum, 1/4 cup water, and salt. Stir to dissolve; set aside. Stir the baking soda into the molasses; set aside. To the shortening mixture, add the liquid ingredients alternating with the dry ingredients scraping down the sides of the bowl as necessary. The dough will be sticky. Transfer to a baking sheet, and cover with plastic wrap. Chill overnight in the refrigerator.
Preheat the oven to 375 degrees. Line baking sheets with Silpats (French nonstick baking mats). Remove dough from refrigerator, and transfer half of the dough at a time to a floured work surface. Roll out dough 1/8-inch-thick. Using a 4-inch round cutter or a large glass, cut out dough rounds. Using a spatula, place cookies 2 inches apart on prepared baking sheets. Bake until the tops begin to crack, 10 to 12 minutes. Repeat with remaining dough. Transfer baking sheets to wire racks to cool completely. Store in an airtight container for up to 3 days.