Preheat your oven to 325 degrees Fahrenheit. Line 24 muffin cups with liners or spray with non-stick cooking spray and set aside.
In a large bowl, mix the 2 cups shredded zucchini, 3 large eggs, 2 cups granulated sugar, ¾ cup vegetable oil, and 2 teaspoons vanilla.
Add the 2 cups all-purpose flour, ⅔ cup unsweetened cocoa powder, 1 teaspoon baking soda, 1 teaspoon salt, and ½ teaspoon baking powder. Spoon the batter into the prepared pans, filling them about halfway.
Bake for 25 minutes or until a toothpick comes out clean. Cool cupcakes on wire racks.
In a large bowl, whisk together the 8 oz room temperature block cream cheese and ½ cup room temperature unsalted butter until creamy.
Add 3 cups powdered sugar, ½ cup unsweetened cocoa powder, ¼ teaspoon salt, and 1 teaspoon vanilla. Continue beating until smooth and whipped. Frost cupcakes.
