Preheat and toast nuts: Preheat the oven to 350°F and line a 9×5-inch loaf pan with parchment leaving an overhang. Spread 1 cup hazelnuts on a baking sheet and toast in the oven for 8–10 minutes until fragrant; cool, then pulse or roughly chop and reserve.

Grate and squeeze zucchini: Grate 2 medium zucchinis on the large holes, place grated zucchini in a clean towel or paper towels, gather edges, and squeeze firmly until the free liquid stops; measure 2 cups packed and set aside.

Mix dry ingredients: In a medium bowl whisk together 1 3/4 cups all-purpose flour, 1 teaspoon baking soda, 1 teaspoon baking powder, 1/2 teaspoon fine salt, and 1 teaspoon ground cinnamon.

Mix wet ingredients: In a large bowl combine 3/4 cup packed light brown sugar and 1/2 cup granulated sugar with 1/2 cup neutral oil; whisk in 2 large eggs and 1 egg white until smooth, then stir in 1 teaspoon vanilla extract.

Combine batter: Fold the dry ingredients into the wet in two additions until just combined. Fold in the squeezed zucchini, 1/2 cup chopped hazelnuts, and 3/4 cup semisweet chocolate chips, reserving a few nuts and chips for the top. If the batter seems very stiff, stir in 1–2 tablespoons milk to loosen.

Fill pan and top: Spoon the batter into the prepared loaf pan, smooth the top, and sprinkle the reserved hazelnuts and a few extra chocolate chips over the surface.

Bake and test for doneness: Bake at 350°F for 48–55 minutes, checking at 45 minutes; the cake is done when a toothpick inserted near the center comes out with a few moist crumbs and the top springs back when pressed. Tent with foil for the last 10–15 minutes if the top browns too quickly.

Cool before slicing: Cool the cake in the pan for 15 minutes, then lift it out using the parchment overhang and cool on a wire rack for about 45 minutes before slicing.