Preheat the oven to 350°F (176°C). Butter and flour a 9.75-inch Bundt cake pan. Tap out the excess flour. Whisk flour, baking powder and salt into a small bowl.
Add yogurt to the milk and use a spoon or fork to mix them together slightly. Set aside.
Place chopped chocolate in a microwave safe bowl and microwave for 30 seconds. Stir, and microwave 10 more seconds. Stir and microwave 5 more seconds. Stir until all the chocolate is melted. Microwave 5 more seconds if needed. Set aside.
In a large mixing bowl, add in butter, oil and sugar. With the paddle attachment, start beating on high speed for 1 minute until light and fluffy.
Reduce the speed to medium. Add the eggs one at a time, mixing well after each addition (about 30 seconds). Scrape the sides of bowl to make sure everything is combined. Add vanilla extract and mix.
Reduce the speed to low, mix in the dry ingredients in 3 parts, alternating with milk and yogurt mixture. Start and finish with the dry ingredients. Do not overmix.
Add 1-1¼ cup of the batter to the melted chocolate and fold it in until mixed.
Alternate adding the chocolate and vanilla batter into the pan. Use a knife and swirl the batter slightly.
Bake in the preheated oven for about 35-45 minutes or until a toothpick inserted in the center comes out clean.
Let the cake cool down in the pan for 30 minutes. Then flip it onto a plate or cake stand.