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 fully combined. Add eggs one at a time, beating well after each addition. Blend in yogurt or sour cream and vanilla extract.
04 - Stir in grated zucchini. Fold dry ingredients into wet mixture until just combined. If desired, gently incorporate chopped nuts.
05 - Transfer batter to prepared pan and spread evenly. Bake 35 to 40 minutes, or until a toothpick inserted in the center comes out clean.
06 - Allow cake to cool 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 has dissolved and mixture gently boils. Continue boiling for 1 minute. Remove from heat and let cool 5 minutes.
08 - Whisk in powdered sugar and vanilla extract until icing is smooth and spreadable.
09 - Spread icing evenly over cooled cake. Allow icing to set before slicing and serving.