01 - Preheat oven to 350°F. Grease and flour a 9x13-inch baking pan.
02 - In a medium bowl, whisk together all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground 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. Blend in yogurt and vanilla extract.
04 - Stir grated zucchini into the wet mixture. Gently fold in the dry ingredient mixture until just combined. Add chopped nuts if using.
05 - Spread the batter evenly in the prepared pan. Bake 35 to 40 minutes, or until a toothpick inserted in the center comes out clean.
06 - Let the cake cool completely in the pan on a wire rack.
07 - In a small saucepan over medium heat, melt unsalted butter. Stir in brown sugar and milk; cook, stirring constantly, until the sugar is dissolved and mixture comes to a gentle boil. Boil gently for 1 minute. Remove from heat and let cool 5 minutes.
08 - Whisk in sifted powdered sugar and vanilla extract until smooth and spreadable.
09 - Spread icing evenly over the completely cooled cake. Allow icing to set before slicing and serving.