Cut the banana into a few pieces and place in the bowl of a food processor along with the brown sugar blend, rum, and banana liquor. Pulse until smooth. Pour in the evaporated milk, low-fat milk, almond extract, and vanilla pudding; pulse until evenly blended. Pour into a bowl and refrigerate at least 30 minutes.
Transfer the chilled banana mixture to the cylinder of an ice cream maker; freeze according to manufacturer's directions.