01 - Preheat oven to 350°F. Grease and flour a 9x13-inch baking pan.
02 - In a bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
03 - In a large bowl, beat vegetable oil, granulated sugar, and brown sugar until well combined. Add eggs one at a time, mixing thoroughly after each addition. Incorporate plain yogurt or sour cream and vanilla extract.
04 - Stir grated zucchini into wet mixture. Fold in dry ingredients just until combined. If desired, gently fold in chopped nuts.
05 - Spread batter evenly in prepared pan. Bake for 35 to 40 minutes or until a toothpick inserted into the center comes out clean.
06 - Allow cake to cool fully in the pan placed on a wire rack.
07 - In a small saucepan, melt unsalted butter over medium heat. Add brown sugar and milk, stirring until sugar dissolves and mixture comes to a gentle boil. Boil for 1 minute, remove from heat, and let cool for 5 minutes.
08 - Whisk in powdered sugar and vanilla until smooth and spreadable.
09 - Spread icing over cooled cake and allow it to set before slicing.