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 vegetable oil, granulated sugar, and brown sugar until combined. Add eggs one at a time, beating thoroughly after each. Mix in yogurt and vanilla extract.
04 - Stir in grated zucchini. Fold in dry ingredients just until combined. If using, gently fold in chopped nuts.
05 - Spread batter evenly in prepared pan. Bake for 35 to 40 minutes, until a toothpick inserted in the center exits clean.
06 - Cool cake completely in the pan on a wire rack before icing.
07 - In a small saucepan over medium heat, melt unsalted butter. Add brown sugar and milk, stirring constantly until sugar dissolves and mixture gently boils. Maintain gentle boil for 1 minute, then remove from heat and cool for 5 minutes.
08 - Whisk in sifted powdered sugar and vanilla extract until icing is smooth and spreadable. Spread icing evenly over cooled cake. Allow icing to set prior to slicing.