How to Make It
To prepare the cake, preheat oven to 350°. Coat a 9x13-inch baking pan with baking spray; set aside.
In a stand mixer fitted with a paddle attachment, beat the butter at medium speed until pale and fluffy, 4-6 minutes. Gradually beat in the granulated sugar and brown sugar at medium speed until well incorporated and fluffy, another 4-5 minutes. With mixer running on medium-low speed, add the eggs one at a time, beating just until the yellow yolk of each egg disappears into the batter. Add the vanilla extract with the final egg.
Whisk together the flour, cornstarch, baking powder, baking soda, salt, cinnamon, ginger, and cardamom in a medium mixing bowl. With mixer running on low speed, gradually add the flour mixture to batter, mixing until just combined. Fold the zucchini into the batter using a rubber spatula.
Pour the batter into prepared pan, smoothing top into an even layer with a rubber spatula. Bake at 350° for 35 to 40 minutes or until a wooden skewer inserted into the center of the cake comes out clean or with only a few moist crumbs. Transfer the cake to a wire rack and cool completely before frosting.
To prepare the frosting, melt the butter in a large skillet or saucepan over medium-low heat; cook, stirring often, until the milk solids turn golden brown and the butter smells nutty. Pour the butter into a large mixing bowl and transfer to the fridge; chill until the butter solidifies, but is still soft, 20 to 25 minutes.
Add the softened cream cheese to the bowl with the butter; beat at medium speed with an electric mixer until smooth and fluffy. Add the powdered sugar and salt; beat at low speed until combined. Fold the chopped pecans into the frosting. Spread the frosting over the completely cooled cake and sprinkle with candied pecans if desired.