Preheat oven to 350 F degrees. Butter and lightly flour an 8x4” loaf pan. Set aside.
In a large bowl, mix together flour, baking powder, baking soda, salt, cinnamon and nutmeg until well combined.
In a separate large bowl, mix together granulated sugar and brown sugar until well combined. Add oil, applesauce, eggs and vanilla and mix until well combined (approximately 1 minute).
Add shredded carrots, zucchini and flour mixture to the liquid ingredient mixture and mix just until combined, do not over mix.
Pour mixture into prepared 8x4” pan. Bake for 35 minutes, then carefully place a sheet of aluminum foil over the top of the loaf pan without removing the pan from the oven, in order to prevent over browning. Continue to bake for an additional 15 - 20 minutes, or until toothpick inserted into center of loaf comes out clean.
Remove from oven and allow to cool in loaf pan for 5 minutes, then invert onto a wire rack and cool completely. If desired, frost with frosting once bread has cooled.