Preheat oven to 180 degrees C. Butter and flour a 23cm cake tin.
Crumb Topping: mix brown sugar, flour, cinnamon and butter with a fork until you have pea size crumbs. Set aside.
Cake: Beat the egg whites until at stiff peaks. Set aside.
In a medium bowl mix the flour and the baking powder together. Set aside.
In the bowl of an electric mixer beat the yolks, butter and sugar on medium-high until it gets pale and creamy. Add the vanilla.
Turn speed to low and slowly add the flour mixture and the milk, alternating between each but finishing with the milk. Fold in the egg whites into the batter.
Pour half of the batter in the prepared tin. Make a layer using half of the bananas and half of the crumb mixture. Pour the remaining batter on top of it and repeat the layer of banana and crumb topping.
Bake in preheated oven until a skewer comes out clean. This cake takes me about 1 hour to bake, so be patient.
Cool it for 15 minutes before slicing it.
A spring form cake tin will make it easier to keep the crumb topping intact and give you a nicer presentation but it's not necessary as you can just take slices straight from the tin.