Preheat oven to 350°F. Grease a bundt pan and set aside.
In a small bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
Using a hand mixer or a stand mixer with the paddle attachment, cream the butter and sugar. Add the Greek yogurt and vanilla extract and mix until combined.
Add the flour mixture in three parts, alternating with the buttermilk; be sure to start and end with the flour mixture. Mix on low speed until batter forms.
Remove one cup of batter and place in a separate bowl. Mix in the melted chocolate until thoroughly combined to make the chocolate batter.
Pour half the vanilla batter into the prepared pan. Top with scoops of the chocolate batter, then pour the remaining vanilla batter on top. Use a knife to swirl (optional). Bake for 35-40 minutes or until a toothpick inserted into the center comes out clean. Allow the cake to cool in the pan for 5-10 minutes before inverting onto a plate or stand.
This recipe was updated in December 2020. The original recipe called for an egg replacer, slightly less sugar, and sour cream instead of Greek yogurt.