Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, beat together the sugar, oil, eggs, and vanilla until smooth. Stir in the grated zucchini.
Add the flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Mix until well combined.
Pour the batter into the prepared pan and spread evenly. Bake for 25 minutes or until a toothpick inserted into the center comes out clean.
While the bars are cooling, prepare the frosting. In a small saucepan, melt the butter over medium heat until it turns golden brown. Remove from heat immediately.
In a mixing bowl, combine the browned butter, powdered sugar, milk, vanilla extract, and salt. Beat until smooth and creamy.
Spread the frosting over the cooled zucchini bars. Cut into squares and serve.
Notes
For a more savory version, reduce the sugar in the bars and increase the salt slightly.