Prepare the layer: start by beating the eggs with the sugar and vanilla. Once they turn into a fluffy cream, spoon by spoon add the flour that you've mixed with the baking powder. Stir this mixture with a spatula from the bottom up, so it doesn't deflate.
Pour and distribute the dough evenly into a large oven tray, covered with baking paper or silicone baking mat. Bake the layer in a preheated 338°F (170 °C) oven until ready. Check to see if ready with a dry toothpick by poking it.
Place the ready layer onto a cooking grid to cool.
Prepare the 2 Dr. Oetker puddings according to packet directions. For the syrup, heat the water, add the sugar and several drops of liquid rum essence. Once the sugar melts, remove syrup from the stove and cool.
Cut the layer into 2, then each of those into halves. Place 1/2 the cake layers into small rectangular forms, syrup them with the prepared syrup.