Start by melting the unsalted butter in a small saucepan over medium heat, stirring occasionally. Once melted, continue cooking until it turns golden brown with a nutty aroma, about 5-7 minutes. Pour into a small bowl and let it solidify at room temperature or in the refrigerator—you need it firm enough to beat with cream cheese later. While the butter cools, preheat your oven to 350°F and prepare a 9x13 inch baking dish by greasing it well and lining it with parchment paper for easy removal.
Finely shred the zucchini using a box grater or food processor, then place it in a clean kitchen towel and gently squeeze to remove excess moisture—this prevents your cake from becoming soggy. In a medium bowl, whisk together the flour, cinnamon, baking powder, sea salt, baking soda, nutmeg, and ginger. I like to sift the spices together first to ensure they're evenly distributed throughout the cake for consistent flavor in every bite.
In a large bowl, whisk together the granulated sugar, neutral oil, room temperature eggs, sour cream, and vanilla essence until well combined. The room temperature eggs are important here—they emulsify better with the oil and create a more tender crumb. Whisk for about 1-2 minutes until the mixture is smooth and slightly pale.
Gently fold the dry ingredient mixture from Step 2 and the prepared zucchini into the wet mixture from Step 3, stirring just until combined—don't overmix or you'll develop too much gluten and create a tough cake. Pour the batter into your prepared pan and smooth the top. Bake for 35-40 minutes, until a toothpick inserted in the center comes out with just a few moist crumbs. The cake should be golden brown and springy to the touch.
Let the cake cool in the pan for 10-15 minutes, then turn it out onto a wire cooling rack to cool completely. This prevents condensation from making the top soggy while still keeping the crumb tender. Let it cool for at least 1 hour before frosting—a warm cake will melt the frosting and make it slide right off.
Once the solidified brown butter from Step 1 is ready, beat it together with the softened cream cheese in a medium bowl using an electric mixer on medium speed for about 2-3 minutes until light and fluffy. The brown butter should be cool but still soft enough to beat easily. Add the sifted icing sugar gradually, alternating with the vanilla extract and kosher salt, beating on low speed between additions to avoid a powdered sugar cloud. Once all ingredients are incorporated, increase speed to medium and beat for another 1-2 minutes until the frosting is creamy and spreadable. I find that adding a pinch of cinnamon to the frosting ties it beautifully to the cake's warm spices.
Spread the brown butter frosting generously over the completely cooled cake from Step 5, using an offset spatula or the back of a spoon to create your desired texture. Decorate as you like—a sprinkle of cinnamon or a drizzle of extra brown butter adds a nice finishing touch. Slice and serve at room temperature for the best flavor.