Preheat the oven to 170°C/340°F. Grease a bundt cake pan and dust it with unsweetened cocoa powder.
Beat the butter until soft and creamy. Add the white sugar and brown sugar and beat well. Add oil and vanilla and beat for 4 minutes. Add the eggs, one at a time, beating after each addition.
In a bowl, sift together flour, baking powder and cocoa powder. Add them to the egg mixture alternating with the yogurt and mix to combine.
Add the zucchini and mix with a wooden spoon. Add the melted chocolate and mix to combine.Pour the batter into the prepared pan and bake for 60 minutes or until a toothpick inserted in the center comes out barely moist. For the ganache: Bring the cream to a boil over low heat. Remove from the heat and add the chocolate. Let it stand for a few minutes and stir until smooth. Once it has cooled and thickened, pour it over the cake.
