||Melt 1 cup of butter. Brush the phyllo dough sheets with the butter. Layer three sheets on top of one another. Cut the phyllo dough in half. Place a peeled banana on each half. Pack brown sugar on the banana. Roll up. Tuck the ends under and brush the outside of the dough with melted butter. Place on a half sheet pan and bake in a 350 degree oven until the dough becomes crispy.
While the banana is baking, combine the cream and remaining butter in a sauce pan and cook over medium heat until the butter is melted and the mixture comes to a simmer. Remove from the heat. In another saucepan, combine the sugar and water and cook over high heat to a medium-dark caramel, washing down the sides of the pan as necessary to prevent crystals from forming. Remove the pan from the heat and while stirring constantly, slowly and carefully pour the warm cream mixture into the caramel. Cool slightly and stir in the dark rum. Cool completely.
When the bananas are cooked, remove from the oven and slice in half on a angle. Rest one half on top of the other and place a large scoop of ice cream in the middle. Pour the caramel rum sauce over the ice cream, garnish with a mint sprig and serve at once.
Toasted Coconut-Rum Ice Cream
Combine Cocoa Lopez, milk and rum in a large bowl and whisk till blended. Chill and add toasted coconut. Process in an ice cream machine according to the manufacturer s instructions.