Add whipping cream, whole milk, and vanilla bean in a pan and simmer for 15 - 20 minutes. Stir constantly and do not cover.
In a separate bowl mix the eggs and sugar until well blended.
After the cream and milk has been simmering, take out the vanilla bean and add the egg/sugar mixture to the pan, maintaining the simmer and the stirring.
When this begins to thicken (approx 3-5 minutes) remove from heat, cover with plastic wrap (tight to the mixture), and put in the fridge until completely
Once cool add the bananas (diced), the mixture, and the vanilla extract into a blender and blend for 4 minutes on high or until it looks slightly frothy.
Immediately (do not let mixture settle) put this in your ice cream machine and chill per the machine's instructions. It will make just under 2 quarts, perfect for a 2 quart machine. Add in the chocolate chips before serving.