In a large saute pan, over medium heat, melt the butter. Add the brown sugar and stir until the sugar dissolves. Add the bananas and cook, stirring for 3 minutes. Remove the pan from the heat and carefully add the liqueur and rum. Return the pan to the stove and carefully ignite the alcohol and shake the pan until the flames die down, about 30 seconds. Remove from the heat and cool completely.
Place the softened ice cream into a large bowl. With a wooden spoon, mix in the cooled banana mixture.
To assemble: Line 1 cup molds with plastic wrap. Spread 3/4 cup of the ice cream over the bottom and sides of the molds. Spoon 1/4 cup of the chocolate mousse in the center of the mold. Fill the mold with the remaining ice cream. Wrap the molds in plastic wrap and freeze until firm.
For the garnish: In a saute pan, over medium heat, melt the butter. Add the sugar and stir to dissolve. Cook the sugar mixture for 1 minute. Add the bananas and continue to cook for 1 minute. Remove from the heat.
To serve, drizzle each plate with the chocolate sauce. Unmold the bombes and place in the center of each plate. Spoon the banana mixture over each bombe and serve immediately.
1 1/2 cups heavy cream
Combine all of the ingredients in a saucepan, over medium heat, and bring to a simmer. Cook until the chocolate melts completely, whisking occasionally. Remove from the heat, pour into a glass bowl and cool completely. Cover with plastic wrap and refrigerate until well chilled. In an electric mixer with a wire whip, beat until the cream forms firm peaks.
Combine the half-and-half and butter in a small heavy-bottomed saucepan over medium heat. Heat the mixture until a thin paper-like skin appears on the top. Do not boil. Add the chocolate and vanilla and stir until the chocolate melts and the mixture is smooth. Remove from the heat and let cool.