01 - Preheat oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan.
02 - Whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg in a bowl.
03 - In a large bowl, beat vegetable oil, granulated sugar, and brown sugar until well combined. Incorporate eggs one at a time, blending thoroughly after each. Mix in yogurt or sour cream and vanilla extract.
04 - Stir in grated zucchini. Fold dry ingredients into wet mixture until just combined. If desired, gently fold in chopped walnuts or pecans.
05 - Spread batter evenly in the prepared pan. Bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
06 - Allow cake to cool completely in the pan on a wire rack before icing.
07 - Melt butter in a small saucepan over medium heat. Add brown sugar and milk, stirring until sugar dissolves. Bring to a gentle boil and cook for 1 minute. Remove from heat and let cool for 5 minutes.
08 - Whisk in sifted powdered sugar and vanilla extract until icing is smooth and spreadable.
09 - Spread icing evenly over cooled cake. Allow icing to set before slicing and serving.