Preheat the oven to 325 degrees F / 165 degrees C. Generously grease a 12-cup / 2.8L and dust with cocoa powder.
In a medium bowl, sift together the flour, baking soda, salt, and 2/3 cup / 50g cocoa powder. Sift to remove any lumps.
In a stand mixer fitted with the paddle attachment, cream the butter on medium-high speed until creamy and smooth, about 1 minute.
Turn the mixer speed to low, add both sugars to the butter, and mix until incorporated. Drizzle in the oil and vanilla, turn the speed to medium-high, and beat until very light and fluffy, about 5 minutes. Scrape the bowl often for even incorporation.
Turn the speed to medium-low and add the eggs, one at a time, beating just until combined. Scrape the bowl after each addition.
Add one-third of the flour mixture to the butter mixture, mixing on low speed, just until combined. Add half the yogurt, mixing until incorporated. Repeat with another one-third flour, then the remaining yogurt, and finish with the final one-third flour, scraping the bowl and paddle after each addition.
Remove the bowl from the mixer and stir in the zucchini until it is evenly distributed. Then add the chocolate and stir until combined.
Pour the batter into the prepared pan. Gently tap the pan on the counter several times to make sure the batter has fully settled into the nooks of the Bundt.
Bake until a tester comes out with moist crumbs, about 1 hour. DO NOT OVERBAKE. Let the cake cool in the pan for 10 minutes, then flip it out onto a serving plate and dust the top with cocoa before serving.