1. In a wide skillet or saucepan, heat the brown sugar with one-quarter of the coconut milk or sour cream, stirring, until smooth and bubbly.
2. Add the bananas and salt, and continue to cook, stirring occasionally, until the bananas are soft and completely cooked through. It should take about five minutes.
3. Remove from heat and stir in the remaining coconut milk or sour cream, rum and vanilla. Taste, and add a few drops of fresh lemon juice if it tastes too sweet.
4. Puree in a blender or food processor until completely smooth.
5. Chill thoroughly, then freeze in your ice cream maker according to the manufacturer’s instructions. (If it’s too thick when you take it out of the refrigerator, whisk it briskly, which should thin it out so you can pour it into your machine.)