01 - Preheat the 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 well mixed. Add eggs one at a time, blending thoroughly after each. Mix in yogurt and vanilla extract.
04 - Stir in grated zucchini until incorporated. Gently fold in the dry ingredient mixture until just combined. Add chopped nuts if desired.
05 - Pour the batter evenly into the prepared pan. Bake for 35 to 40 minutes, or until a toothpick inserted in the center emerges clean.
06 - Allow the cake to cool completely in the pan on a wire rack.
07 - In a small saucepan, melt unsalted butter over medium heat. Add brown sugar and milk, stirring until the sugar dissolves and mixture comes to a gentle boil. Continue boiling for 1 minute. Remove from heat and let cool for 5 minutes.
08 - Whisk in powdered sugar and vanilla extract until the icing is smooth and spreadable.
09 - Spread icing evenly over the cooled cake. Allow icing to set before slicing and serving.