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 homogenous. Add eggs one at a time, beating well after each addition. Mix in yogurt or sour cream and vanilla extract until smooth.
04 - Stir grated zucchini into wet mixture. Gently fold in prepared dry ingredients just until combined. If using, fold in chopped nuts.
05 - Spread batter evenly into prepared pan. Bake 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
06 - Cool cake completely in the pan on a wire rack.
07 - In a small saucepan, melt butter over medium heat. Add brown sugar and milk, stirring constantly until sugar dissolves and mixture gently boils. Continue boiling for 1 minute. Remove from heat and let cool for 5 minutes.
08 - Whisk powdered sugar and vanilla extract into cooled mixture until icing is smooth and spreadable.
09 - Spread icing over cooled cake. Allow icing to set before slicing and serving.