1. Preheat oven to 325 degrees and lightly grease and flour a 9 x 5 loaf pan.
2. In a large mixing bowl, beat eggs lightly. Add oil, mashed bananas, grated zucchini, and vanilla and beat.
3. In a separate bowl, measure dry ingredients and stir to combine.
4. Add dry ingredients to the egg mixture. Stir just until all ingredients are moistened.
5. Spoon into loaf pan.
6. Bake at 325 degrees for 50 minutes. Test for doneness by inserting a toothpick in the center. It should come out dry.
7. Allow loaf to cool 5 to 10 minutes before turning out onto a cooling rack.
8. Serve warm or allow to cool before slicing.