Preheat oven to 400 degrees F. To make the biscuits, add together the diced cheese, Bisquick and sugar, mix well. Add the water and mix thoroughly to make a wet batter. Drop the batter in 4 mounds onto a greased cookie sheet and bake on the top rack for 20 minutes or until cooked through (when toothpick inserted in middle comes out clean). Remove from oven and cool on wire rack.
To make the sauce, melt the butter in a saucepan and saute the bananas for about 3 minutes. Add the sugars and stir until melted. Add the cream and, stirring constantly, cook over high heat until it reaches a boil. Reduce the heat to low and cook for 10 minutes. Add the rum and banana liqueur.
To serve, cut the cooled biscuits from the top two thirds of the way down, open it up and pour the sauce into the center of the biscuit. Serve with whipped cream and mint sprig. Serves 4.