Completely submerge gelatin sheet in a bowl of cold water and let sit until soft. Whip egg yolk in electric mixer on high speed until it thickens. Add sugar to water and cook until it starts to bubble. Add cooked sugar to yolk, keeping the machine on high speed. Melt softened gelatin in microwave for 15 seconds on low heat. Add melted gelatin, then mascarpone into yolk mixture. Fold in whipped cream and thoroughly mix, being careful not to over mix.
Slice Bananas and sauté in butter, sugar and vanilla beans until golden brown. Whisk egg whites with sugar until stiff peaks form. Stir in egg yolks and fold flour into mixture. Spread batter evenly in a half-sheet baking pan. Bake at 350° F for approximately 15 minutes. Cool to room temperature.
Spread half of mascarpone mousse on cooled sponge cake. Layer caramelized bananas on top of mousse. Layer remaining mascarpone mousse over bananas. Put in freezer, freeze until set and serve.
Garnish with caramelized bananas and chocolate pieces.