In a small bowl, stir together the rum, water and salt until the salt dissolves. In a medium bowl, whisk together the flour, ginger, allspice, nutmeg, and cloves. In a large measuring cup, stir together the molasses and baking soda (the mixture will begin to bubble), and let sit approximately 15 minutes until doubled in volume.
With an electric mixer on medium-high speed, beat together the butter and sugar approximately 2 minutes until fluffy. Reduce the speed to medium-low and gradually beat in the rum mixture. Add the flour mixture and the molasses mixture, alternately in two batches; scraping the sides of the bowl as needed. Cover the bowl with plastic wrap and refrigerate until stiff, at least 8 hours or up to 3 days.
Preheat oven to 375 degrees F. Adjust two oven racks to the upper-middle and lower-middle positions. Line two baking sheets with parchment paper.
Working with half of the cookie dough, which will be soft) at at time on a heavily floured work surface, roll out the dough to 1/4-inch thick. Cut out the cookies with a 3- to 3 1/2-inch cookie cutter or the rim of a drinking glass. Space the cut out cookies 1 1/2-inch apart on the prepared baking sheets (only 6 cookies per baking sheet as they will spread).
Bake approximately 6 to 7 minutes, switching and rotating the baking sheets halfway through baking, or until the cookies are set and just beginning to crack. Remove from the oven and let the cookies cool on the baking sheets for 10 minutes, then transfer to a wire rack to cool completely.
Repeat with the remaining dough using a fresh or cooled baking sheet.
Refrigerated dough stays fresh about a week, frozen dough three months.
The cookies can be stored in an airtight container for up to 1 week.
Joe Frogger Cookies Recipe: https://whatscookingamerica.net/cookie/joefroggercookies.htm