Position a rack in the middle of the oven and preheat to 350°F. Grease an 8 by 4 by 2-inch loaf pan with nonstick baking spray and line it with a piece of parchment paper, leaving at least a 2-inch overhang on both longer sides.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, salt, and nutmeg until combined.
In a large bowl and using a handheld mixer, beat the eggs on high speed until frothy, about 1 minute. Add the granulated sugar and beat on high to incorporate, about 1 minute.
With the mixer running on medium-high speed, add the oil in a steady stream and beat until the mixture has the thickness and texture of mayonnaise, about 1 minute. Add the vanilla and beat until incorporated, about 15 seconds. Add the dry ingredients to the wet ingredients and mix on low speed just to combine. Using a rubber spatula, fold in the zucchini just until combined—the batter will be very thick.
Transfer the batter to the prepared loaf pan and smooth the top.
Bake for 1 hour to 1 hour 15 minutes, until a toothpick or cake tester inserted into the center comes out clean and the loaf starts to pull away from the sides of the pan. Let cool in the pan on a wire rack for 15 minutes, then use the overhanging parchment to lift the bread from the pan and set it on the rack. Let cool completely, ideally overnight, before slicing and serving (letting it rest really helps set the bread’s texture).