Preheat oven to 350 degrees F. In a 2 quart bowl, beat eggs. Add brown sugar, nutmeg, 1 teaspoon cinnamon, vanilla, and milk. Break up bread in a 9 x 13 pan. Pour egg mixture over bread. Push down with a fork until most of liquid is absorbed. Sprinkle with the remaining 1 teaspoon of cinnamon. Bake for 1 hour ot until it is golden brown. Allow to cool. Next place bananas on top of bread pudding. Make pudding according to box and then pour over the top of bread pudding and bananas. Cover the entire top of bread pudding with the whipped topping. Keep refrigerated.