Preheat the oven to 350°F and grease a 9×13-inch baking pan or line it with parchment; grate the zucchini using a box grater or food-processor attachment, place in a clean dish towel, and squeeze until no more water drips (about 20–30 seconds).

In a medium bowl whisk together the flour, cornstarch, cinnamon, nutmeg, baking soda, baking powder, and salt until evenly combined.

In a large bowl whisk the granulated sugar, brown sugar, and eggs until combined; stir in the oil, yogurt (or sour cream), and vanilla until smooth.

Fold the dry ingredients into the wet ingredients until just combined, then gently fold in the squeezed zucchini and the optional chopped nuts; avoid overmixing to keep the cake tender.

Scrape the batter into the prepared pan, smooth the top, and bake at 350°F for 35–45 minutes, checking at 35 minutes; a toothpick should come out with a few moist crumbs but not wet batter.

Let the cake cool in the pan on a wire rack for 20 minutes, then invert onto the rack and cool completely before frosting.

Beat the softened cream cheese and butter together until smooth; add the powdered sugar and vanilla and beat until combined; add 1 to 2 tablespoons milk if needed to reach spreadable consistency.

Spread the cream cheese frosting over the completely cooled cake with an offset spatula; chill briefly if the frosting needs to set before slicing and serving.