Prepare a heritage bundt cake pan, or any other bundt cake pan of your choice. Grease it thoroughly so that no dry spots are left.
Preheat the oven to 180°C (top and bottom heating).
Place eggs with sugar and vanilla extract in a bowl of a stand mixer and beat for 10 minutes on low-medium speed. Sift the two combined flours and baking powder oven the mixture, combine gently with a spatula, then mix on a medium mixer speed for about 30 seconds.
In a small pot, melt butter and oil together. Make sure not to overheat them and chill slightly (the temperature of the mixture should be low enough to touch it with bare hand). Slowly pour butter and oil into the dough, mix for a minute on medium speed until the ingredients are combined.
Melt the chocolate in a water bath, set aside to cool.
Pour ½ of the dough into a separate bowl, add chilled melted chocolate and a spoon of cocoa. Mix everything together just until incorporated.
Pour half the dough without chocolate at the bottom of the bundt cake pan. Using an ice cream spoon, scoop out the entire chocolate part of the dough on top, then pour out the remaining dough without chocolate.
Put in the oven preheated to 180°C. Bake for 45 minutes (or until a toothpick inserted into the cake comes out dry). Take out of the oven with the open pan side up and set aside to cool completely.