First, begin preparation of the layers: Beat the eggs in a large bowl with the sugar until you get a creamy mixture. Combine the flour and baking powder and add them gradually, while beating nonstop with the mixer on the lowest setting.
Add the oil and lemon zest. Stir everything well and pour it into a rectangular oven dish, laid out with baking paper. Bake in a preheated 392°F (200 °C) oven for about 25 min.
Check with a toothpick to make sure the cake layer is fully baked. Once it is, take it out and leave it to cool. Once cooled enough, cut it into 2 separate, identical layers.
While waiting for the cake layer to cool, begin preparation of the cream: mix the flour with a little water. Pour the milk into a pot and put it on the stove.
Add the sugar and stir until it melts. Once the milk starts boiling, add the flour in a thin trickle, while stirring energetically the entire time. Once the cream thickens, take it off the stove. Add the vanilla and stir again.
For the syrup: combine the milk and water in a pot, put on the stove, add the sugar. Once it starts boiling, add the cocoa, stir well to dissolve it.
Start assembling the cake: Put the lower cake layer in the oven dish in which you baked it, pour on half the syrup. Then arrange pieces of chopped banana and pour on half the cream. Place the 2nd cake layer, syrup again and pour on cream. Finally, sprinkle with ground walnuts.
Leave the cake overnight or at least 5 hours in the fridge before serving.