Preheat oven to 350°F (175°C). Grease a 9×5-inch loaf pan.
In a bowl, whisk flour, baking soda, baking powder, cinnamon, nutmeg, and salt.
In another large bowl, beat eggs, sugar, oil, and vanilla until smooth.
Stir in grated zucchini and apple.
Add dry ingredients to wet ingredients; stir until just combined.
Pour into loaf pan and bake 50–60 minutes, or until a toothpick inserted in the center comes out clean.
Cool in pan 10 minutes, then transfer to a wire rack.
Note:
This bread freezes well—wrap cooled slices in plastic wrap and store in a freezer bag for up to 3 months. You can also add ½ cup chopped nuts or raisins for extra texture. For best flavor, use a sweet apple variety like Honeycrisp or Fuji.