In a food processor, combine all ingredients until smooth. Pour into an ice cream maker and process until firm. If you do not have an ice cream maker, pour the mixture into a glazed stoneware mixing bowl that has been chilled thoroughly in the freezer. Cover with plastic wrap and place in freezer until firm.
Melt butter in pan. Add brown sugar and stir until smooth. Add sliced bananas and continue cooking, stirring frequently, for 3-4 minutes. Spoon bananas and sauce over sorbet.