Preheat the oven to 350°F (175°C). Grease and flour a 9×13-inch sheet pan.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, and salt. Set aside.
In a large bowl, beat the granulated sugar, brown sugar, and creamy peanut butter until creamy and well combined.
Add the vegetable oil, eggs, and vanilla extract to the peanut butter mixture and beat until smooth.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Fold in the shredded zucchini and semisweet chocolate chips until evenly distributed.
Pour the batter into the prepared sheet pan and spread evenly.
Sprinkle the chopped peanuts evenly over the top, if using.
Bake for 30 to 35 minutes or until a toothpick inserted in the center comes out clean.
Allow the cake to cool completely in the pan on a wire rack before cutting into squares and serving.