Preheat the oven to 350°F. Lightly coat a standard 12-cup muffin pan with nonstick spray or line each cavity with cupcake liners for easy removal.
In a large mixing bowl, whisk together the dry ingredients: all-purpose flour, wheat bran, unsweetened cocoa powder, baking soda, and kosher salt. Stir until the mixture is uniform and free of clumps.
In a separate medium-sized bowl, combine the eggs, buttermilk, sugar, canola oil, and vanilla extract. Whisk until the mixture is smooth and the eggs are fully incorporated.
Create a well in the center of the dry ingredients. Gradually pour in the wet mixture, whisking gently until just combined—be careful not to overmix, as this may result in dense muffins.
Fold the grated zucchini and ¼ cup of the chocolate chips into the batter, stirring just until evenly distributed. Divide the batter evenly among the prepared muffin cups, filling each with approximately ⅓ cup of the mixture.
Sprinkle the remaining ¼ cup of chocolate chips over the tops of the muffins for a rich, melty finish. Bake in the preheated oven for 25 to 30 minutes, or until a toothpick inserted into the center comes out mostly clean with a few moist crumbs.
Let the muffins cool in the pan for 10 minutes before carefully removing them using a small offset spatula. Transfer to a wire rack and allow to cool completely before serving. The result is a moist, chocolatey muffin with hidden veggie goodness and bursts of melted chocolate in every bite.