Preheat your oven to 350°F (177°C). Line the bottom of an 8- or 9-inch round cake pan with parchment and lightly grease the sides.
In a medium bowl whisk together the flour, baking powder, cinnamon, salt and chopped walnuts. Set aside.
In a large bowl, beat the eggs, extra yolk and granulated sugar with a hand mixer or whisk until the mixture becomes pale and slightly thickened, about 3–4 minutes.
Slowly pour the melted butter into the egg mixture while stirring constantly, then stir in the vanilla. Fold in the squeezed grated zucchini until evenly distributed.
Add the dry ingredient mixture to the wet ingredients and gently fold with a spatula just until no streaks of flour remain — do not overmix.
Transfer the batter to the prepared pan, smooth the top, and tap the pan on the counter once to settle the batter.
Bake in the center of the oven for 45–55 minutes, or until the top is golden and a toothpick inserted near the center comes out clean or with just a few moist crumbs. If the top browns too quickly, tent loosely with foil after 30 minutes.
Let the cake cool in the pan on a wire rack for about 10 minutes, then run a knife around the edge and invert onto the rack to cool completely.
Once cooled, dust the cake with powdered sugar before slicing and serving.