In a large mixing bowl, combine flour, cocoa powder, baking soda, baking powder, espresso powder if using, and salt. Mix well and set aside.
In another bowl, whisk together oil, granulated sugar, brown sugar, eggs, sour cream, and vanilla extract until smooth and well combined. A hand mixer or stand mixer works best for this.
Add the shredded zucchini to the wet mixture and stir gently to incorporate. Gradually mix in the dry ingredients until just blended; the batter will be thick.
Carefully fold in the chocolate chips to distribute them evenly throughout the batter.
Divide the batter between the prepared pans and smooth out the tops. Bake for 28 to 32 minutes, checking for doneness by pressing lightly on the tops; it should spring back or a toothpick should come out clean.
Let the cakes cool in the pans on a wire rack for about an hour. Once cooled, remove from pans, peel off parchment, and cool completely before frosting.