01 - Preheat oven to 350°F. Grease and flour a 9x13-inch baking pan.
02 - In a medium 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 smooth. Add eggs one at a time, beating thoroughly after each addition. Mix in yogurt and vanilla extract.
04 - Stir in finely grated zucchini. Fold the prepared dry ingredients into the wet mixture until just combined. If using, 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 in the center comes out clean.
06 - Allow cake to cool completely in pan on a wire rack before icing.
07 - In a small saucepan over medium heat, melt butter. Add brown sugar and milk, stirring constantly, and bring to a gentle boil. Boil for 1 minute, remove from heat, and cool for 5 minutes.
08 - Whisk in sifted powdered sugar and vanilla extract until icing is smooth and spreadable.
09 - Spread icing evenly over the fully cooled cake. Allow icing to set before slicing and serving.