Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 10-inch Bundt pan.

Stir cake mix and pudding mix together in a large bowl. 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 the preheated oven until a skewer inserted into the cake comes out clean, about 50 to 55 minutes. Let cool in pan for 10 minutes, then turn out onto a wire rack and cool completely.

To make the glaze: Combine confectioners’ sugar, milk and vanilla in a small bowl. Whisk until smooth and a drizzling consistency. When cake is cooled, drizzle icing over cake with a zigzag motion. Sprinkle chopped nuts over wet icing if desired.