01 - Preheat oven to 350°F. Lightly grease and flour a 9x13-inch baking pan.
02 - In a medium bowl, whisk together all-purpose flour, baking powder, baking soda, salt, cinnamon, and nutmeg until thoroughly blended.
03 - In a large bowl, beat vegetable oil, granulated sugar, and brown sugar until completely incorporated. Add eggs one at a time, beating well after each addition. Mix in yogurt and vanilla extract until smooth.
04 - Stir grated zucchini into the wet mixture. Fold in the flour mixture until just combined, ensuring not to overmix. Gently fold in chopped nuts if desired.
05 - Spread batter evenly into prepared baking pan. Bake for 35 to 40 minutes, or until a toothpick inserted into the center emerges clean.
06 - Allow cake to cool entirely in the pan on a wire rack before icing.
07 - In a small saucepan over medium heat, melt butter. Stir in brown sugar and milk, cooking and stirring until sugar fully dissolves and mixture reaches a gentle boil. Boil for 1 minute, then remove from heat and let cool 5 minutes.
08 - Whisk in sifted powdered sugar and vanilla extract until icing is smooth and spreadable.
09 - Evenly spread icing over completely cooled cake. Allow icing to set before slicing and serving.