Preheat your oven to 350°F or 177°C. Grease a 13x9-inch pan with oil.

Whisk all the all-purpose flour, ground cinnamon, nutmeg, baking powder, baking soda, and salt in a large bowl. Put aside.

In another mixing bowl, combine brown sugar, granulated sugar, eggs, oil, applesauce, and pure vanilla extract.

Add the wet ingredients to the bowl of dry ingredients and stir until incorporated. Toss in the shredded zucchini and mix until well combined.

Pour the batter into the greased pan and bake it for 45 to 50 minutes. After 30 minutes, drape aluminum foil over the cake to ensure even baking. If a toothpick inserted in the cake is clean or comes with only a few crumbs, the cake is ready.

Pop it out of the oven and let it cool completely on a wire rack.

Grab a heatproof bowl and put it aside. Toss 4 sticks of unsalted butter, about ¼ cup, in a saucepan or a light-colored skillet (to see the butter browning better). Turn on the stove and stir it constantly on medium heat.

When the butter melts and foams, simmer it for another 5 to 7 minutes. The butter will brown with amber specks formed and a nutty aroma.

Once you see it transform from amber to golden and caramel-brown, turn off the stove and pour the butter into the prepared bowl immediately, scraping up any brown specks from the bottom of the skillet. Let it rest for about 10 minutes, and then place it in the fridge to solidify.

Toss the solidified butter into a large mixing bowl and beat it on high using an electric stand or handheld mixer with a whisk or paddle attachment until smooth and creamy. Fold in 8 ounces of cream cheese until incorporated. Scrape down the bowl while mixing.

Add confectioners' sugar, salt, and pure vanilla extract and mix them on low for around 30 seconds and then on high for another 2 minutes. Layer the frosting on the cake, slice, and enjoy!