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.
03 - In a large bowl, beat vegetable oil, granulated sugar, and brown sugar until thoroughly combined. Add eggs one at a time, mixing well after each addition. Stir in yogurt and vanilla extract.
04 - Fold grated zucchini into the wet mixture. Gradually add the dry ingredients, mixing until just combined. Gently fold in the chopped nuts, if using.
05 - Spread the batter evenly into the prepared baking pan. Bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
06 - Allow the 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, and continue stirring until sugar dissolves and mixture reaches a gentle boil. Boil for 1 minute. Remove from heat and let cool 5 minutes.
08 - Whisk in powdered sugar and vanilla extract until smooth and spreadable.
09 - Spread icing evenly over the cooled cake and allow icing to set before slicing.