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 until thoroughly blended.
03 - In a large mixing bowl, beat vegetable oil, granulated sugar, and brown sugar until smooth. Add eggs one at a time, beating well after each. Blend in yogurt and vanilla extract.
04 - Stir in grated zucchini. Gently fold in the dry mixture until just combined. If desired, incorporate 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 pan on a wire rack.
07 - In a saucepan, melt unsalted butter over medium heat. Stir in brown sugar and milk. Bring mixture to a gentle boil, stirring constantly, and cook for 1 minute. Remove from heat and cool for 5 minutes.
08 - Whisk in sifted powdered sugar and vanilla extract until smooth and spreadable.
09 - Spread icing evenly over the completely cooled cake. Let icing set before slicing and serving.