"Traditional affogato is vanilla gelato topped with espresso, but here a tropical sorbet forms an island in a coffee-flavored rum sea. Rum-based Tia Maria® coffee liqueur is preferred for its wonderful rich flavor."
Place banana slices, pineapple chunks, and cream of coconut in a blender; blend until sorbet mixture is smooth and creamy.
Freeze sorbet in an ice cream maker according to manufacturer's instructions, or pour into a freezer-safe container and freeze, stirring every 30 minutes to break up large ice crystals, until firm, up to 2 hours.
Coil lemon peel into a cylinder and secure with 1 toothpick. Insert mint leaves through the top to create "pineapple" leaves.
Mix coffee liqueur and dark rum together in a coupe glass.
Place a 2-ounce scoop of sorbet in a coupe glass. Pour coffee liqueur and rum mixture on top. Insert 1 toothpick into the center of the sorbet scoop. Place the "pineapple" garnish on top.