In a saucepan over medium heat, combine cream, banana puree and 2 T. sugar. Cook, stirring occasionally until small bubbles appear around edges of pan. Set aside.
In a bowl, beat egg yolks and vanilla until smooth and light. Pour hot cream mixture into egg yolks, a little at a time, beating continuously until well blended. Strain mixture through a fine sieve into a bowl. Divide mixture among 4 ramekins.
Arrange ramekins in a baking pan and place on middle shelf of preheated oven. Fill pan with boiling water to halfway up sides of ramekins. Cover pan loosely with aluminum foil. Bake until custard is just set, about 25 minutes. (this took an additional 9 minutes for mine, as I have deeper ramekins) Chill 2-3 hours.
Slice bananas horizontally into 1/2" slices and arrange on top of chilled creme brulees. Sprinkle remaining sugar over tops of bananas. With cooking torch, move flame econtinuously over the surface of the ramekins, in a circular motion until sugar melts and becomes golden brown and bubbly. (this is where I failed. I was afraid to add the entire 1/3 cup sugar, so didn't get enough carmelized effect) Serve immediately.