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 together vegetable oil, granulated sugar, and brown sugar until well blended. Add eggs one at a time, mixing thoroughly after each addition. Blend in yogurt and vanilla extract.
04 - Fold grated zucchini into wet mixture, then add the dry ingredients, stirring just until combined. Gently fold in chopped nuts if desired.
05 - Spread batter evenly into prepared pan. Bake for 35–40 minutes, or until a toothpick inserted into the center emerges clean.
06 - Allow cake to cool completely in the pan on a wire rack.
07 - In a small saucepan, melt butter over medium heat. Stir in brown sugar and milk; cook, stirring constantly, until sugar dissolves and mixture comes to a gentle boil. Simmer gently for 1 minute. Remove from heat and allow to cool 5 minutes.
08 - Whisk powdered sugar and vanilla extract into cooled mixture until icing is smooth and spreadable.
09 - Spread icing evenly over completely cooled cake. Allow icing to set before slicing and serving.