Molasses-spice cookies date back to the Colonial era, but this variation with rum in the batter comes from Marblehead, Massachusetts. Locals say the cookies are named after Joseph Brown, a free African American man who served in the Revolutionary War and opened a tavern in town. Brown's wife, Lucretia Brown, did the cooking, and these cookies, made in an iron skillet, were her specialty. According to Marblehead Myths, Legends, and Lore by Pam Matthias Peterson, “when the batter hit the pan, it ran in all directions and formed shapes that looked like a frog's body and legs.” Given their shape and the fact that the tavern was next to a frog pond, the name stuck.
In a small bowl, combine hot water and rum. In a large second bowl, whisk together 3 cups flour with the salt and spices. Set aside.
In another large bowl, cream together butter and sugar until light and fluffy, about 4 minutes.
Add water and rum to creamed mixture and beat well. Add one-third of the flour mixture and stir, then stir in half the molasses, scraping down the sides as you go. Repeat with an additional third of the flour mixture and the remaining molasses. Finally, add the rest of the flour mixture. If dough seems too loose, add the extra ½ cup flour.
Divide the dough into two balls, cover with plastic wrap, and chill at least 45 minutes and up to overnight.
Preheat oven to 375° and grease two baking sheets or line with parchment.
You have two options for shaping the cookies: On a floured surface, you can roll the dough out to a ½-inch thickness and use a floured 2-inch cookie cutter or drinking glass to cut the dough into rounds. Transfer the cookies to the prepared baking sheets, leaving about 2 inches between cookies. Alternately, you can skip the rolling and instead break walnut-sized pieces of dough and roll them into balls between your palms. Arrange the balls on the baking sheet and put some granulated sugar into a bowl. Press the bottom of a drinking glass into the sugar, then press it onto each ball of dough, flattening it before baking.
Bake the cookies until they have set but still seem soft in the middle, about 10 minutes. Cool on wire racks.