Boil the milk with the cinnamon stick; add the tapioca pearls.
Cook on medium heat stirring occasionally (more often in the last 10 minutes) for approx. 25 minutes until the pearls are completely translucent.
In a small frying pan melt the butter, add the bananas and a pinch of cinnamon and fry for 3-4 minutes.
Divide the tapioca and fried banana between 4 serving jars or glasses by arranging them in the following way in each glass: put a layer of tapioca and layer of fried bananas, repeat and top up with fruit.