Place the banana chunks in the bowl of a food processor and pulse a few times, until the banana is in small pieces. Add the remaining ingredients and process until smooth and creamy, stopping several times to scrape the bottom of the bowl with a rubber spatula. Add water a teaspoon at a time if necessary to help the processor. Divide ice cream among molds or holes in an ice tray, or just scoop it into bowls. If using molds, freeze until solid before serving.