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Preheat the oven to 350°. Generously butter six 4-ounce ramekins with 2 tablespoons of the butter.
In a small bowl, mix the flour with the baking soda. In another bowl, using an electric mixer, beat the remaining 4 1/2 tablespoons of butter until creamy. Add the light brown or turbinado sugar and beat until light and fluffy. Add the eggs, 1 at a time, and beat until just incorporated. Beat in the mashed bananas. Using a large spatula, fold the dry ingredients into the batter until incorporated.
Spoon the batter into the ramekins and set them in a baking pan. Carefully pour enough hot water into the pan to reach halfway up the sides of the ramekins. Bake for 40 minutes, or until the cakes are firm but spring back when pressed lightly with your finger.
Remove the pan from the oven and transfer the ramekins to a rack with tongs; let cool slightly. Run a sharp knife around the sides of the cakes, then invert them onto a wire rack to cool while you prepare the sauce.
In a medium saucepan, combine the butter with the sugar, rum and water and bring to a boil, stirring constantly to dissolve the sugar. Remove from the heat.
Spoon some of the sauce onto plates. Set the cakes on the sauce, spoon the rest of the sauce on top and serve.