01 - Preheat oven to 350°F. Grease and flour a 9x13-inch baking pan.
02 - In a bowl, whisk flour, baking powder, baking soda, salt, cinnamon, and nutmeg until well blended.
03 - With an electric mixer or whisk in a separate large bowl, beat together vegetable oil, granulated sugar, and brown sugar until fully incorporated. Add eggs one at a time, mixing thoroughly after each. Stir in plain yogurt or sour cream and vanilla extract until smooth.
04 - Stir finely grated zucchini into wet mixture. Gradually fold in dry ingredients until just combined. If desired, add chopped nuts.
05 - Spread batter evenly in prepared pan. Bake for 35 to 40 minutes, or until a toothpick inserted in the center emerges clean.
06 - Allow cake to cool completely in the pan on a wire rack.
07 - In a saucepan over medium heat, melt butter. Add brown sugar and milk, stirring until dissolved. Bring mixture to a gentle boil and cook for 1 minute. Remove from heat and let cool for 5 minutes.
08 - Add powdered sugar and vanilla extract to the saucepan. Whisk until smooth and spreadable.
09 - Spread icing evenly over cooled cake. Allow icing to set before slicing for serving.