With a small knife remove the hard bit of stem at the tip of each fig. Place the figs in a small saucepan with the rum and water. Bring to a boil over high heat. Cover pan, reduce heat to simmer and continue cooking until figs are tender, about 20 minutes. Set aside. Grease botton and sides of a round baking pan 23 cm in diameter and 5 cm high with shortening or vegetable oil. Line the bottom with a circle of parchment or aluminum foil. Set aside. Cut the chocolate into small pieces and melt it with the butter in the top of a double boiler. (I use a microwave). Remove from heat and stir until smooth. Crack the eggs into a large bowl. Add cocoa and sugar to the eggs and beat with an electric mixer until blended evenly. Drain the figs, discarding the liquid. Stir figs and chocolate into the egg mixture and mix well. Spoon the batter into the prepared pan. Bake in a preheated 350 degree oven until the cake rises to the top of the pan and feels set in the center, about 40 minutes. Let it cool in the pan on a wire rack. When cool, turn it out onto a rack. Remove the parchment or foil, invert the cake into a large serving plate. Cover it and refrigerate until ready to serve. Accompany with whipped cream.