Preheat oven to 350 degrees F. Grease a 9 x 13 inch (23 x 33 cm) baking dish.
In a large bowl, beat eggs, sugars, and oil until light and airy. Add vanilla, and mashed bananas and beat until smooth and creamy. Stir in the flour, baking powder, baking soda, salt, and cinnamon until just combined. Fold in the chopped walnuts.
Pour the batter into the prepared baking dish and bake for 30-40 minutes, or until a wooden skewer inserted in the center comes out clean. Let the cake cool in the pan for 10 minutes before turning it out onto a wire rack to cool completely. (You can also leave the cake in the baking dish for easy serving or transport)
For the frosting: use an electric mixer to beat cream cheese in a medium bowl until fluffy. Add confectioner's sugar and beat until smooth. Spread over cooled cake. Top with additional chopped walnuts.