01 - Preheat oven to 350°F. Grease and flour a 9x13-inch baking pan.
02 - In a mixing bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
03 - In a large mixing bowl, beat together vegetable oil, granulated sugar, and brown sugar until well combined. Incorporate eggs one at a time, mixing thoroughly after each addition. Blend in yogurt and vanilla extract.
04 - Stir grated zucchini into the wet ingredients. Gently fold in the dry mixture until just combined. If desired, fold in chopped walnuts or pecans.
05 - Spread batter evenly into the 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, melt butter over medium heat. Add brown sugar and milk, stirring continuously until the sugar dissolves and mixture reaches a gentle boil. Boil gently for 1 minute, then remove from heat and let cool for 5 minutes.
08 - Whisk in sifted powdered sugar and vanilla extract until the icing is smooth and spreadable.
09 - Spread icing evenly over cooled cake and allow it to set before slicing.