A rich puree of Medjool dates gives this cakelike pudding a wonderful, deep flavor -- perfect with the rich toffee sauce that slicks the surface of the dessert.
Preheat oven to 350 degrees. Make the pudding: Butter an 8-inch square cake pan; set aside. Put dates, rum, and 1/2 cup water into a small saucepan. Bring to a boil over medium-high heat, stirring occasionally. Reduce heat to medium-low; cover, and simmer until dates are very soft, about 5 minutes.
Carefully transfer date mixture to a food processor, and puree (you should have about 1 cup). Let cool 15 minutes.
Whisk together flour, baking powder, salt, cinnamon, and baking soda in a medium bowl; set aside.
Put butter and brown sugar into the bowl of an electric mixer fitted with the paddle attachment. Mix on medium-high speed until pale and fluffy, about 2 minutes. Add eggs, one at a time, mixing well after each addition and scraping down sides of bowl as needed.
Reduce speed to low. Add flour mixture in 3 additions, alternating with the date puree. Transfer batter to prepared pan; smooth top. Bake 25 minutes. Reduce temperature to 325 degrees, and bake until a cake tester inserted into center of pudding comes out clean, 15 to 20 minutes. Let cool in pan on a wire rack 5 minutes. Run a knife around edges of pan to loosen, and invert onto a serving plate.
Make the sauce: Put cream, brown sugar, and butter into a medium saucepan. Bring to a boil over medium-high heat. Cook 3 minutes. Stir in rum, and cook 1 minute more (you should have about 1 1/2 cups sauce). Pour half of the sauce over pudding. Serve immediately with remaining sauce on the side.