To begin, preheat your oven to 350 and line a loaf pan with parchment paper, with two edges sticking out for easy removal.
To a large mixing bowl, add your butter and sugar and beat together with a mixer till creamy. To the same bowl, add Greek yogurt, milk and vanilla and mix till smooth. Add your eggs and briefly blend it in.
To the same bowl add your flour, baking soda and salt. Add your cocoa powder through a fine mesh strainer to the bowl as well. Stir everything together till well combined (You should have a thick batter).
To the same bowl, add your shredded zucchini (patted dry between two towels) and your chocolate chips, and fold them into the batter.
Pour into your loaf pan. Bake in the oven for 60-65 minutes, or till a toothpick inserted comes out clean, and the top is springy to touch.
Let cool entirely before slicing. Then devour!