Preheat oven to 250 degrees.
In medium bowl with an immersion blender, beat together rum, cream, milk, egg yolks and sugar until smooth. Beat in ripe bananas and blend until smooth.
Divide into four ramekins.
Place filled ramekins into 13x9 inch pan. Fill pan half way with water. Transfer whole dish set up to oven and allow to bake for 1 Hour and 15 minutes.
Remove ramekins from oven and water bath and allow to cool. Place into fridge for at least two hours to cool. Or overnight.
When ready to serve, sprinkle remaining baker's sugar over the creme brulee and place all ramekins under broiler until sugar caramelizes.
Serve and devour immediately.
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