In a medium baking dish toss the bananas, butter, and 1/2 cup brown sugar. Bake for about 40 minutes, or until soft and caramelized.
Pour the bananas and gathered syrup into a blender. Add the milk, cream, salt, vanilla paste, and remaining sugar. Puree until very smooth.
Cover and chill the mixture for at least 8 hours. Pour into an ice cream maker and freeze according to the manufacturer’s directions. During the last minutes of churning sprinkle in the chopped chocolate and bourbon.
Transfer to an airtight container, press plastic wrap against the ice cream, and freeze until firm, at least 2 hours. The flavor will ripen the longer the ice cream freezes!
Notes
Note: the mixture MUST BE COLD before it goes into the ice cream maker. If it's too warm, it will remain soupy and never churn into thick ice cream.