Step 1

Preheat oven to 350°. Spray two 8 1/2x4 1/2" loaf pans with nonstick spray and line with parchment paper, leaving a generous overhang on long sides. If using, spread walnuts on a rimmed baking sheet and toast until slightly darkened and fragrant, 8–10 minutes; let cool, then coarsely chop.

Step 2

Whisk eggs, oil, granulated sugar, brown sugar, and vanilla in a large bowl until smooth. Whisk flour, salt, cinnamon, baking soda, baking powder, and nutmeg in another large bowl just to combine. Make a well in the center of dry ingredients, add egg mixture, and slowly incorporate dry ingredients with a fork (batter will look dry). Fold in zucchini, walnuts, and 1 cup oats. Scrape batter into prepared pans.

Step 3

Toss raw sugar and remaining 1/4 cup oats in a small bowl. Sprinkle over batter and bake until a tester inserted into the center comes out clean, 70–80 minutes. Transfer pans to a wire rack and let bread cool in pans 30 minutes; turn out bread onto rack and let cool completely.

Step 4

DO AHEAD: Bread can be baked 4 days ahead. Store tightly wrapped at room temperature.