Special equipment: an ice cream maker
For the banana ice cream: Stir together the bananas, brown sugar and honey in a medium pot over medium heat. Cook, stirring occasionally, until the sugar is dissolved, the mixture begins to caramelize and the bananas begin to break down, 4 to 5 minutes.
Combine the half-and-half, milk, vanilla and salt in a large measuring cup or container and pour slowly into the banana mixture. Stir until combined. Chill the ice cream base 2 hours and up to overnight. Freeze in an ice cream maker according to the manufacturer's instructions. Transfer to a freezer-safe container and freeze to set.
For the fudge sauce: Combine the condensed milk and chocolate in a small saucepan over medium-low heat and cook, stirring, until the chocolate is melted and the mixture is combined. Remove from the heat and whisk in the butter and vanilla. (Makes 2 cups.)
Serve the banana ice cream with the fudge sauce.