Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 10 inch Bundt pan.
In a large bowl, stir together cake mix and pudding mix. Make a well in the center and pour in eggs, water, oil and mashed banana. Beat on low speed until blended. Scrape bowl, and beat 4 minutes on medium speed. Pour batter into prepared pan.
Bake in a preheated oven for 50 to 55 minutes, or until cake tests done. Let cool in pan for 10 minutes, then turn out onto a wire rack and cool completely.
To make glaze: In a small bowl, combine confectioners' sugar, milk and vanilla. Whisk until smooth and of a drizzling consistency. When cake is cooled, drizzle icing over cake with a zigzag motion. Sprinkle chopped nuts over wet icing if desired.