Preheat oven to 350 degrees. Grease two 9x5-inch loaf pans with cooking spray and line with parchment paper; set aside. In a large bowl, stir together the flour, baking powder, baking soda, salt and dry pudding mix; set aside. In a separate medium bowl, whisk together the eggs and sugar until thick and lemon color. Stir in the vanilla and oil. Last, stir in the shredded zucchini. Then, add the wet ingredients to the dry ingredients and stir together until just combined. Batter will be a weird green color, but it won't look like that after baking.
Divide batter between the two prepared loaf pans. Bake for 55 minutes or until a toothpick inserted in the center comes out clean. The center will most likely sink, but that's okay. Cool in pans for 10 minutes, then remove loaves from pans and cool completely. Slice each loaf into 10 slices and serve.