Prep the pan and oven: Heat oven to 350°F (175°C).
Grease a 9x13-inch baking pan and line the bottom with parchment for easy removal.
Prep the zucchini: Wash and trim the ends. Grate on the medium holes of a box grater. Lightly blot with a paper towel if extremely wet, but do not squeeze dry.
You want that moisture.
Combine dry ingredients: In a large bowl, whisk flour, cocoa, baking powder, baking soda, salt, and espresso powder until evenly mixed.
Mix the wet ingredients: In a separate bowl (or the bowl of a stand mixer), whisk sugar, eggs, oil, yogurt, and vanilla until smooth and slightly thick, about 1–2 minutes.
Bring it together: Add the dry ingredients to the wet and stir gently until most of the flour streaks disappear. The batter will be thick.
Bloom the cocoa: Pour in the hot coffee (or water) and stir until the batter loosens and turns glossy. Scrape down the bowl as needed.
Fold in the zucchini and chips: Add the shredded zucchini and chocolate chips.
Fold just until evenly distributed. Avoid overmixing.
Bake: Pour the batter into the prepared pan and smooth the top. Bake for 30–38 minutes, or until a toothpick inserted near the center comes out with a few moist crumbs, not wet batter.
Cool: Set the pan on a rack and let the cake cool completely before frosting.
This helps the crumb set and keeps the frosting from melting.
Make the frosting (optional): Beat butter until creamy. Sift in powdered sugar and cocoa, then add vanilla, salt, and 2 tablespoons milk. Beat until fluffy, adding more milk as needed for a spreadable texture.
Frost the cooled cake.