Preheat your oven to 350°F (175°C). Line two 9×5-inch loaf pan with parchment paper and set aside.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon and allspice. Set aside.
In a separate bowl, mix the melted butter, oil, granulated sugar, brown sugar and applesauce until smooth and well combined.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Fold the shredded zucchini into the wet mixture until evenly distributed.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top.
Bake for 55–65 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for 15 minutes, then transfer to a cooling rack to cool completely before slicing.