Preheat the oven to 350 degrees F.
Brush a 14-inch oval baking dish with 2 tablespoons of butter. In a large bowl whisk together the eggs, 1 cup brown sugar, cream, and milk. Add the vanilla, cinnamon, cherries, bread, and chocolate, and stir to blend thoroughly.
Set a 10-inch saute pan over medium-high heat and add the 2 tablespoons of the room temperature butter to the pan; once melted, add the diced bananas to the pan and saute for 3 minutes. Add the remaining 1/4 cup brown sugar to the pan and saute until the sugar is melted, about 2 minutes. Remove the pan from the heat and add the rum and banana liqueur to the pan. Return the pan to the heat and ignite the alcohol. Once the flames die out, fold the bananas into the bread pudding base. Stir the remaining 2 tablespoons butter into the mixture and pour into the baking dish.
Bake until firm, about 1 hour. Remove from the oven and allow to cool on rack until just warm. Place a square of the pudding down on the plate, with a scoop of the Drunken Monkey Ice Cream. Drizzle the Chocolate Sauce over the ice cream and bread pudding and garnish with the mint leaves and powdered sugar.
In a small, heavy saucepan, bring the cream to a bare simmer over low heat. Place the chocolate pieces in a medium bowl. Pour the cream over the chocolate and let sit for 2 minutes. Whisk in the vanilla and continue whisking until the sauce is smooth and thickened. Let the sauce cool to room temperature before serving.
In a 2-quart saucepan set over medium heat, add the milk, cream, vanilla bean, pod seeds and the banana. In a medium-sized bowl, combine the sugar and egg yolks and beat, using a whisk, until pale yellow and smooth. Pour about 1 cup of the milk and cream mixture into the egg yolk mixture and whisk thoroughly. Add the egg yolk mixture to the saucepan and simmer gently, stirring with a wooden spoon. Be sure to stir inside the corners of the pan. As the custard cooks, it will thicken, and be able to coat the back of a spoon. This will take about 5 minutes. Remove the custard from the heat and strain through a fine mesh sieve, into a clean non-reactive bowl.
Add the white chocolate to the custard and stir to melt the chocolate. Once the chocolate is melted, pour the rum into the bowl and stir well to blend. Refrigerate the custard and allow it to chill for at least 2 hours before proceeding.
Once the custard is cool, pour the ice cream base into an ice cream maker, and follow the manufacturer's instructions on how to properly freeze the custard. When the ice cream is partially frozen, add the cashew brittle to the base and continue to churn the machine.
While the ice cream is churning, melt the chocolate with the vegetable oil over a double boiler. Stir the chocolate as it melts to keep it smooth. Once the chocolate is completely melted, drizzle it into the ice cream. As the hot chocolate hits the cold cream, it will cool and form into shards. Continue to churn the ice cream until it is nearly completely frozen. Remove from the machine and place in an airtight container. Freeze for at least 4 hours, and preferably overnight.
In a saucepan combine the sugar, water and corn syrup. Set over a medium heat, and cook until the sugar turns a caramel color, and a candy thermometer inserted into the sugar registers 280 degrees F. Whisk the butter into the sugar, and remove from the heat. Stir the pan vigorously until the butter has completely dissolved and the sugar is a deep amber color. Add the cashews and baking powder to the pan and continue to stir quickly to ensure that the cashews are well distributed in the sugar. Pour the brittle onto a greased baking sheet and when cool, about 30 minutes, crack into 1/4-inch pieces using a rolling pin.