Preheat oven to 350°F. Line an 8- or 9-inch square baking pan with parchment leaving an overhang, then lightly grease the paper and sides.
In a medium bowl whisk together the flour, baking powder, baking soda, cinnamon, salt, and nutmeg until evenly combined; set aside.
In a separate large bowl whisk the Greek yogurt, maple syrup, avocado oil, eggs, and vanilla until smooth and slightly glossy.
Stir the dry ingredients into the wet mixture in two additions, folding gently with a spatula until just combined — do not overmix.
Fold in the drained grated zucchini, chocolate chips, and chopped walnuts until evenly distributed. Let the batter sit for 8–10 minutes to hydrate the flour and relax the texture.
Scrape the batter into the prepared pan and smooth the top with an offset spatula. Sprinkle the surface with the extra chocolate chips and turbinado sugar.
Bake in the center of the oven for about 30 minutes, rotating the pan once at the 15-minute mark, until the top is golden and a toothpick inserted in the center comes out clean or with only a few moist crumbs.
Cool the cake in the pan on a wire rack for 15 minutes, then use the parchment overhang to lift it out and transfer to the rack to cool completely before slicing into 12 squares.
Serve room temperature or lightly warmed; store leftovers wrapped in the refrigerator for up to 4 days or freeze individual squares for longer storage.