Lightly grease a 15x10x1-inch baking pan. Line bottom with parchment paper or waxed paper; grease paper. Set aside. In a medium mixing bowl stir together flour, baking powder, and baking soda; set aside.
For filling, in a small mixing bowl combine cream cheese and the 1/2 cup granulated sugar; beat with an electric mixer on medium speed until smooth. Add whole egg and milk; beat until combined. Spread in the prepared pan; set aside.
In a medium mixing bowl beat egg yolks and vanilla on medium speed about 5 minutes or until thick and lemon colored. Gradually add the 1/3 cup granulated sugar, beating until sugar is dissolved. Stir in banana and nuts.
Thoroughly wash the beaters. In a large mixing bowl beat the egg whites on medium speed until soft peaks form (tips curl). Gradually add the 1/2 cup granulated sugar, beating on high speed until stiff peaks form (tips stand straight). Fold yolk mixture into egg whites. Sprinkle the flour mixture evenly over egg mixture; fold in just until blended.
Carefully spread the batter evenly over the filling in the pan. Bake in a 375 degree F oven for 15 to 20 minutes or until the top springs back when lightly touched.
Immediately loosen cake from sides of pan and turn out onto a towel sprinkled with powdered sugar. Carefully peel off paper. Starting with a short side, roll up cake, using towel as a guide but not rolling towel into cake. Cool completely on rack.
Spread top with Vanilla Cream Cheese Frosting. If desired, drizzle with chocolate-flavored syrup. Makes 10 servings.
Vanilla Cream Cheese Frosting
In a small mixing bowl combinecream cheese, softened, and vanilla; beat with an electric mixer on medium speed until light and fluffy. Gradually beat in unsifted powdered sugar. Beat in enough milk to make a frosting of spreading consistency. Makes about 1/2 cup frosting.