In a large bowl, combine the pudding mixes,milk and whipping cream, and beat at high speed until very thick and beaks form when beaters are lifted. Set aside.
In a small pan, prepare the chocolate sauce. Combine all of the ingredients together except for the egg yolk, and cook over a low heat just until melted. Once melted, slowly whisk in the beaten egg yolk. Let the chocolate sauce cool until lukewarm.
Mix the cooled espresso coffee and rum together Completely submerge the lady fingers, one a a time, but do not let sit, then layer in the bottom of a 10 inch springform pan. Cut the cookies if necessary to fill in all of the spaces.
Spread half of the pudding mixture over the layer of cookies. Repeat the dipped lady fingers, then spread the remaining pudding over the lady fingers and smooth as evenly as possible.
Pour the sauce over the cake (sauce will be runny), and refrigerate overnight. Remove from the springform pan just before serving.
Note: If the egg yolk cooks while being whisked into the chocolate sauce, simply strain it before pouring over the cake.