Zucchini and Ginger Naked Cake with Ginger Cream Cheese Frosting

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Cake:

Unsalted butter, for the pans

3 1/2 cups all-purpose flour, plus more for the pan 

1 1/2 pounds zucchini 

2 teaspoons baking powder 

1 1/2 teaspoons baking soda 

1 1/4 teaspoons salt 

1 1/2 teaspoons ground cinnamon 

1 teaspoon ground ginger 

1/2 teaspoon ground cloves 

2 cups light brown sugar 

4 large eggs 

1 1/3 cups vegetable oil 

3/4 cup whole milk 

1 1/2 tablespoons finely grated fresh ginger

1 1/2 teaspoons vanilla extract 

Frosting:

24 ounces cream cheese, softened

2 sticks (1 cup) unsalted butter, softened 

6 cups confectioners' sugar 

1/2 cup finely chopped crystallized ginger, plus a few pieces sliced into thin strips, for garnish