Sift together flour, baking powder, baking soda, salt, and vanilla pudding mix in a medium bowl; set aside.
Step 3
Beat sugar and shortening in a large bowl with an electric mixer until light, scraping the sides of the bowl often. Add eggs one at a time, beating well after each addition. Mix in milk.
Step 4
Add flour mixture and mashed banana alternately to creamed mixture, beating until smooth after each addition. Fold in nuts. Pour batter into the prepared loaf pan.
Step 5
Place in a cold, non-preheated oven. Set the temperature to 350 degrees F (175 degrees C). Bake for 50 minutes. Cover loaf loosely with foil to prevent burning and continue baking until a toothpick inserted into the center comes out clean, 10 to 20 minutes more. Let loaf rest in the pan for 10 minutes, then remove to a wire rack to cool completely.