Preheat oven to 325°F (163°C). Grease two 8x4-inch loaf pans generously with butter or nonstick spray, or line with parchment paper with overhang for handles. Place pans on a baking sheet.
Wash the zucchini but do not peel. Grate using the large holes of a box grater or food processor shredding disc. Measure 2 cups of grated zucchini, packing lightly without squeezing out moisture.
In a medium bowl, whisk together flour, salt, baking soda, baking powder, and cinnamon until well combined, about 30 seconds.
In a large bowl, lightly beat the eggs. Whisk in granulated sugar and brown sugar for 1-2 minutes until combined. Add vegetable oil and whisk until smooth and emulsified. Stir in vanilla extract.
Add the grated zucchini to the wet ingredients and stir with a spatula until evenly distributed, breaking up any large clumps.
Pour the flour mixture over the wet ingredients and fold gently with a spatula just until no dry flour streaks remain, about 15-20 folds. Do not overmix.
Divide the batter evenly between the prepared pans, filling each about two-thirds full. Smooth the tops and tap the pans on the counter 2-3 times to release air bubbles.
Bake on the center rack for 50-60 minutes, checking at 50 minutes with a toothpick. It's done when the toothpick comes out with a few moist crumbs (not wet batter) and the tops are golden brown.
Cool in the pans on a wire rack for 15-20 minutes. Run a knife around the edges, then turn the loaves out onto the rack. Cool completely, 1-2 hours, before slicing.