Line a 9x5-inch loaf pan with parchment paper, leaving overhang on the sides for easy removal. Spray with nonstick cooking spray.
In a medium saucepan over medium heat, melt the butter and oil together. Remove from the heat and stir in the cocoa powder until smooth and glossy. Stir in the espresso powder. Allow to sit and cool for a few minutes while you prepare the dry ingredients.
In a large bowl, whisk together the flour, baking soda, baking powder, and salt. Toss in the grated zucchini until evenly coated.
To the butter-cocoa mixture, whisk in both sugars. Add the eggs and vanilla, stirring until fully incorporated. Pour wet ingredients into the flour mixture, stirring until just combined. Fold in most of the semi-sweet chocolate chips and milk chocolate chips, reserving a few tablespoons for the top. Let batter sit for 15 minutes while oven is preheating.
Preheat oven to 350ºF. Pour batter into loaf pan, smoothing out the top. Evenly sprinkle the reserved chocolate chips over the batter. Bake for 1 hour, or until a toothpick inserted in the center comes out clean. Allow to cool in pan for 30 minutes.
Run a butterknife along the sides of the pan to release bread from pan and use the parchment sides to lift the bread out and onto a cooling rack. Allow to cool 20 more minutes. Slice, serve, and enjoy!
Notes
*There's no need to blot or wring out zucchini. I also used the large (standard) holes of a cheese grater to shred my zucchini.