How to Make It
Preheat oven to 350°F. Place overripe bananas on a baking sheet. Bake in preheated oven 10 minutes. Remove from oven, and cool 15 minutes. Peel bananas, reserving both flesh and peels separately.
Combine roasted banana peels and cream in a medium saucepan; bring to a simmer over medium. Remove from heat, and cool to room temperature, about 30 minutes. Pour cream mixture through a fine wire-mesh strainer into the bowl of an electric stand mixer; discard peels. Set mixing bowl in a larger bowl filled with ice water. Let stand, stirring occasionally, until cream is cold.
Remove bowl from ice bath, and return to stand mixer. Add vanilla bean paste to cream; beat at high speed until medium peaks form. Cover and chill until ready to serve.
Combine brown sugar and water in a large skillet over medium-high; bring to a simmer, and stir in butter. Add roasted banana flesh and rum; cook, stirring often, to cook off the alcohol, about 2 minutes. Remove from heat, and stir in lemon juice to taste. Transfer banana mixture to a blender, and blend until smooth. Cool completely.
Layer cake cubes, banana puree, sliced banana, whipped cream, and candied peanuts in individual trifle glasses.