Place top oven rack in the center position and pre-heat oven to 325 F. Generously grease two 9-inch loaf pans with butter and set aside
In a large mixing bowl, beat together the eggs, vegetable oil, applesauce, sugar, brown sugar, and vanilla extract just until blended.
Add the flour, cinnamon, allspice, baking soda, baking powder, and salt to a medium bowl and stir to combine.
Pour the dry ingredients into the wet, a little at a time, and mix to combine. Scrape the sides of the bowl with a spatula, as needed, to make sure the dry ingredients are thoroughly incorporated into the batter.
Add the shredded zucchini and one cup of pecans to the mixing bowl and fold into the batter.
Divide the batter between the prepared loaf pans and place in the preheated oven for 15 minutes. Remove from the oven and sprinkle the remaining pecans on top of each pan.
Return to oven and bake for another 30 minutes before checking for doneness by inserting a toothpick into the center of each loaf. If necessary, continue baking until the toothpick comes out clean. (Depending on how much moisture is in the zucchini, it may take an hour or slightly longer for the loaves to finish baking).
Remove from oven and cool for several minutes. When cool enough to handle, transfer the loaves to a wire rack or cutting board. Slice and serve immediately or cover tightly with plastic wrap once cooled and store in the refrigerator until ready to serve.