Preheat the oven to 325 degrees F. Line 2 cupcake pans with paper liners.
In a large mixing bowl, add 2 cups all-purpose flour, 2/3 cup unsweetened cocoa powder, 1 teaspoon baking soda, 1/2 teaspoon baking powder, and 1/4 teaspoon salt. Whisk until thoroughly combined and set aside.
In a separate mixing bowl, add the 3/4 cup butter, 1 cup granulated sugar, and 1 cup light brown sugar. Beat with a hand mixer on medium speed until creamed.
Add the 3 large eggs, 2 cups shredded zucchini, and 2 teaspoons vanilla extract. Beat with the hand mixture until the eggs are incorporated and the zucchini is evenly distributed.
Add the bowl of dry ingredients into the wet ingredients and beat until a smooth batter forms and the dry ingredients are incorporated.
Fill each cupcake liner half full with the cake batter.
Place in the preheated oven and bake about 23 - 27 minutes,or until a toothpick inserted into the center of one of the middle cupcakes comes out clean or with moist crumbs.
Allow the cupcakes to cool in the pans for 5 minutes before removing the cupcakes and placing on a wire rack to cool completely.
Once the cupcakes are cooled, use an apple corer, small paring knife, or a large piping tip to remove the center of the cupcake making sure to not go all the way to the bottom of the cupcake though. Leave some cake underneath the hole as we will be filling each cupcake with frosting.
Peanut Butter Frosting
In a large mixing bowl add the 1/2 cup creamy peanut butter, 4 ounces cream cheese, and 1/3 cup butter. Beat with a hand mixer on medium speed until creamed.
Add the 1 1/2 cups powdered sugar, 1 tablespoon milk, and 1/2 teaspoon vanilla extract. Beat on low until most of the powdered sugar is worked into the frosting. Turn the mixer to medium speed and continue to beat for 30 seconds to 1 minute until the frosting is light and fluffy. If the mixture is too thick add one to two teaspoons of milk until you reach the desired piping consistency.
Fill a disposable piping bag fitted with the #336 piping tip with the peanut butter frosting.
Fill the center of each cupcake with the frosting.
Pipe swirls of frosting on top of each cupcake.
Store in an airtight container at room temperature.
Notes
Storage: Place the cupcakes in an airtight container at room temperature for up to 4 days. Freezing: Freeze the cooled and frosted chocolate zucchini cupcakes for up to 3 months in a freezer container or freezer bag. I would only freeze unfrosted cupcakes in the freezer bag. Thaw on the counter for 1 to 2 hours before enjoying.