01 - Preheat 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 until evenly combined.
03 - In a large bowl, beat vegetable oil, granulated sugar, and brown sugar until homogeneous. 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 dry ingredients gently until just incorporated. If using, fold in chopped walnuts or pecans.
05 - Spread batter evenly in the prepared pan. Bake 35 to 40 minutes, or until a toothpick inserted in the center emerges clean.
06 - Allow cake to cool completely in the pan on a wire rack.
07 - In a small saucepan, melt butter over medium heat. Stir in brown sugar and milk. Cook, stirring constantly, until sugar dissolves and mixture gently boils. Maintain boil for 1 minute, then remove from heat and cool for 5 minutes.
08 - Whisk in sifted powdered sugar and vanilla until smooth and spreadable.
09 - Spread icing over cooled cake. Allow icing to set before slicing and serving.