Spread the banana chunks out on a tray and transfer to the freezer. Leave the banana in the freezer until frozen all the way through (about one hour).
Place the frozen banana chunks into a food processor. Add the vanilla, sugar or sweetener and half of the buttermilk. Turn on the processor and blend for a few moments. Then, while it is still running, pour in the remaining buttermilk in a thin, steady stream.
Blend until the mixture is smooth and creamy. Serve at once.