Whisk the eggs with sugar and vanilla into the foam and gradually add the flour mixed with the baking powder alternately with milk and vegetable oil. Put the prepared dough on a 9" x 13" baking tray. Grease the baking tray and sprinkle with coarse flour (you can also use baking paper). Bake in a pre-heated oven at 350 °F / 175 °C until golden, for about 30 min. Remove the baked dough and make holes with the other side of the wooden spoon. Let it cool.
Prepare the vanilla pudding. Add sugar to taste (according to how sweet cake you prefer). Lay the pudding smoothly on the cake and let it cool down.
Heat the cream over low heat, but do not cook it. Once the cream is warm enough, remove from heat and add the chopped chocolate. Melt it and layer on a cool pudding. Refrigerate and then serve. Enjoy!