Make the Cake: Preheat the oven to 325°. Butter and flour a 9-by-3-inch round cake pan and line the bottom with parchment paper. Butter and flour the paper. In a medium microwave-safe bowl, cover the dates with the rum, espresso and water and heat at high power for 2 minutes. Transfer to a food processor and let stand until the dates are softened. Puree until smooth.
In a bowl, whisk both flours with the baking soda, cinnamon, nutmeg, cloves and salt. In another bowl, using an electric mixer, beat the butter and brown sugar until fluffy. Beat in the eggs until incorporated, then beat in the date puree. Add the dry ingredients all at once and beat at low speed until incorporated.
Scrape the batter into the prepared pan and bake in the center of the oven for 1 hour, until a toothpick inserted in the center comes out clean. Let cool for 15 minutes, then invert the cake onto a rack to cool completely.
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Make the Caramel: In a medium saucepan, simmer the sugar and water over moderate heat until a deep-amber caramel forms, about 6 minutes. Remove from the heat and add the cream. Cook over low heat, stirring, until the hardened caramel is dissolved.
Cut the cake into wedges and serve with the caramel sauce.