Preheat the oven to 200°C / 400°F
Toss the banana pieces with the brown sugar and butter in a large baking dish.
Roast for 40 minutes, stirring once during baking, until the bananas are browned and very soft.
Scrape the bananas and the thick syrup in the baking dish into a blender or food processor - be sure to do this immediately so that the caramelized sugar doesn't have a chance to harden.
Add the milk, granulated sugar, vanilla, lemon juice, and salt, and puree until smooth.
Chill the mixture thoroughly in the refrigerator, then pour it into your ice cream maker, according to the manufacturer’s instructions. If the chilled mixture is too thick to pour into your machine, whisking well before pouring.