Beat 4 eggs + 1 cup sugar in a large bowl until you get a fluffy white cream. Sift 1 cup flour, mix it with 1 vanilla and 1 baking powder, add this to cream.
Smear a suitable baking form with oil and sprinkle with flour, so the layer doesn't stick. Pour the mixture in it. Bake at 392°F (200 °C) until it gains a brown crust on top and turns yellow on the inside. Take the cake layer out and leave it to cool completely, covered with a towel, so it's easier to unstick from the form.
In a pot, heat 1 cup water and 2 cups sugar, pour in 5 drops of rum essence or 2 tbsp of actual rum and 1 vanilla. Heat until the syrup thickens.
Take the cake layer out of the form and cut it in 2 to obtain 2 thinner ones. Soak the cold layers with the warm syrup and smear them with several spoons of the sweetened yoghurt.
Arrange the banana slices on top and pour on a few more spoons of yoghurt.
Place the 2nd layer on top and poke holes in it in several spots with a fork. Smear the sides of the cake with the yoghurt using a brush and pour on the remaining yoghurt over the entire cake.
Leave it in the fridge overnight.