Preheat the oven to 350 degrees F.
Line a muffin pan with paper liners. Set aside.
In a large bowl whisk the butter, milk, eggs, vanilla, and sugars until well combined.
In a medium bowl mix together the flour, cocoa powder, baking powder, baking soda and salt.
Add the dry ingredients to the wet and stir until just combined.
Gently stir in the grated zucchini and chocolate chips.
Scoop the batter into the prepared muffin pans until the cups are 3/4 full.
Sprinkle with coarse sugar and place a few chocolate chips on each muffin.
Bake for 30-35 minutes.
Allow to cool 5 minutes in the pan before removing to a wire rack to cool completely.