Preheat oven to 350°F. Grease 2 9x5-inch loaf pans. Set aside.
In a large bowl, whisk eggs, mashed banana, sugar and oil until well-combined.
Add flour, baking powder, baking soda, cinnamon, and salt. Stir just until combined.
Fold in zucchini just until incorporated.
Pour into greased 9x5 loaf pans.
Bake until a toothpick inserted in center comes out clean, about 45-50 minutes.
Cool in pans for 10 minutes before removing to wire racks to cool completely.
Mashed ripe bananas: The best bananas to use for banana bread are slightly overripe bananas. The bananas should be yellow with plenty of brown speckles.
All-purpose flour: It's important to properly measure the flour. Weighing it will give you the best and most accurate results. If you aren't weighing the flour, sift or stir it to break it up. Lightly spoon it into the measuring cup and level. Too much flour will give you dry or dense, heavy bread.
Shredded zucchini: There's no need to peel or squeeze the zucchini.
If the bread is browning too quickly, tent with aluminum foil.