Preheat oven to 350°. Grease 2 loaf pans (9 in.). In a large bowl, beat eggs until frothy. Add sugar, oil, zucchini, and vanilla and stir until well mixed. Add flour, cinnamon, salt, baking powder, baking soda, and nuts; stir until just combined.
Pour batter into pans. Bake until a toothpick inserted in the center of each loaf comes out clean, 50 to 60 minutes. Cool loaves 10 minutes in pans, then turn out onto a rack and cool completely before slicing.
Note: Nutritional analysis is per serving.