Preheat oven to 400 degrees F. Line a baking pan with aluminum foil. Set aside.
In a mixing bowl gently combine bananas, figs, melted butter, and dark brown sugar. The fruit needs to be well coated with the melted butter and brown sugar.
Pour fruit mixture onto prepared baking pan. Spread fruit around the pan into a single layer. Place pan on a middle rack in the preheated oven and bake for approximately 30 minutes, stirring halfway through cooking time.
Remove pan and stir the fruit once more. At this point the fruit can be left on the pan to cool or it can be transferred to a plate or bowl for cooling. I chose to transfer the fruit to a plate for quicker cooling. Cool completely before proceeding with the remainder of the recipe.
In a separate bowl, mix together the half and half, heavy cream, sweetened condensed milk, sugar, vanilla, and cinnamon. Whisk until the ingredients are well combined and the sugar has dissolved.
Transfer the fruit to a blender. Pour a little of the ice cream base into the blender. The liquid ice cream base will help the fruit to puree more easily. Pulse blend the fruit until smooth, adding a little more ice cream base if necessary.
Transfer the contents of the blender back into the bowl with the remainder of the ice cream base. Stir well to combine.
Pour the mixture into the bucket of your ice cream machine. Process according to the manufacturer's directions for your machine.
After processing, the ice cream will be very soft. Transfer it into a bowl or other container, cover, and place in freezer for about 8 hours to allow ice cream to ripen (see notes).