Preheat oven to 300° F.
Whisk together egg yolks and 1/4 cup whipping cream and set aside.
Combine 1 1/4 cups whipping cream and 1/3 cup sugar in a heavy saucepan. Cut vanilla bean in half lengthwise, scrape seeds into saucepan, and add vanilla bean halves.
Bring vanilla mixture to a boil over medium/high heat. Remove from heat and discard vanilla bean.
Whisk about one-fourth of hot mixture gradually into yolk mixture, add to remaining hot mixture, whisking constantly. Skim air bubbles from top of mixture. Pour mixture into an 8-inch square pan. Place into a 13 x 9-inch pan. Add hot water to larger pan to a depth of l inch.
Bake for 35 minutes. Remove pan from water, and cool. Cover and chill at least 2 hours.
Raise oven temperature to 375° F.
Melt 1/2 cup butter.
Stack phyllo, brushing each sheet with butter and sprinkling with powdered sugar. Cut phyllo stack into 16 (3-inch) squares.
Place squares on a parchment paper lined baking sheet. Cover with a sheet of parchment paper and top with another baking sheet.
Bake for 20 minutes or until golden. Remove from oven, and cool to room temperature.
Cook remaining 1 cup sugar and remaining 1/4 cup butter in a small heavy saucepan over medium heat, stirring until butter melts. Slowly add remaining 1 cup whipping cream, and cook, stirring constantly, 8 to 10 minutes or until caramel color. Set aside.
Cut chilled custard into 6 squares. Place one square on each of 6 dessert plates. Top each square of custard with 1 phyllo square. Drizzle a small amount of caramel sauce around custard.
Stir together banana and remaining caramel sauce. Spoon evenly over phyllo squares. Top each with a second phyllo square, and garnish, if desired. Reserve remaining phyllo squares for other uses.
Makes: 4