Place egg whites in a large bowl and egg yolks in a medium bowl; let stand at room temperature for 30 minutes. Meanwhile, coat a large rimmed baking sheet with cooking spray. Line bottom of pan with parchment paper. Coat parchment paper with cooking spray; set aside. In a small bowl, stir together cake flour, baking powder and salt; set aside.
Preheat oven to 350°F. Add flavoring (or vanilla) to the egg yolks; beat with an electric mixer on high speed for about 5 minutes or until thick and lemon-colored. Gradually beat in ¼ cup sugar, beating on high speed until sugar is almost dissolved. Sprinkle flour mixture over egg yolk mixture; gently fold in just until combined. Thoroughly wash the beaters. Beat egg whites with the mixer on medium speed until soft peaks form (tips curl). Gradually beat in the remaining ¼ cup sugar, beating until stiff peaks form (tips stand straight). Fold ½ cup of the beaten egg whites into the egg yolk mixture to lighten. Fold in the remaining egg whites. Spread batter evenly in the prepared pan.
Bake for about 12 minutes or until cake springs back when lightly touched. Immediately loosen the edges of the cake from the pan; turn the cake out onto a clean dish towel. Remove parchment paper. Starting from a short side, roll the towel and cake into a spiral. Cool on a wire rack.
In a medium bowl, whisk together milk and pudding mix just until thickened. Fold in whipped topping. Cover and chill for at least 1 hour.
Unroll the cooled cake; remove towel. Spread the filling to within 1 inch of edges. Thinly slice one of the bananas over the filling. Roll up the cake. Cover and chill for at least 2 hours or up to 8 hours. To serve, thinly slice the remaining banana. Top the cake roll with the sliced banana and sliced strawberries. Drizzle with chocolate syrup.
Tips: We do not recommend using a sugar substitute for this recipe.