Slice the banana into chunks and put them into a freezer-proof container. Put the container into the freezer and leave overnight or until frozen solid.
When ready to make the ice cream, put the frozen banana pieces into a food processor and pulse to break them up into small pieces. Scrape down the sides of the food processor, then blend until the banana is smooth and creamy, stopping regularly to scrape down the sides.
Eat immediately for a soft-serve consistency or put it back into a freezer-proof container and freeze for 1 hour until hard.