Preheat an oven to 350 degrees F (175 degrees C). Prepare 2 8x4-inch loaf pans with cooking spray.
Beat the eggs in a mixing bowl with an electric mixer until frothy. Slowly add the sugar while continually beating. Stir the vegetable oil and vanilla into the egg mixture; continue beating until the mixture is thick. Add the zucchini to the mixture and stir.
Mix the flour, cinnamon, baking soda, baking powder, and salt together in a separate bowl; pour into the wet mixture and stir until just combined. Add the chopped walnuts and stir. Divide the batter between the two prepared loaf pans.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour. Cool in the pans for 10 minutes before loosening the edges with a knife and removing to cool completely on a wire rack.
