Preheat oven to 350F and generously grease and flour cake pans. Set aside.
Place chopped chocolate in a microwave-safe bowl and microwave for 30 seconds. Stir well, and then return to microwave and heat in 15-second increments, stirring well in between, until the chocolate is completely melted and smooth. Set aside.
Using an electric or stand mixer, cream together butter, oil, and sugar until light and fluffy.
Add eggs, one at a time, beating well after each addition. Pause as needed to scrape down the sides and bottom of the bowl then stir in vanilla extract.
In a separate, medium-sized bowl, whisk together flour, baking powder, and salt.
Using a spatula and gently hand-mixing, alternate adding flour mixture and buttermilk to the butter/oil batter, starting and ending with flour mixture and mixing until just combined after each addition.
Pour 1/3-1/2 of the batter into a separate bowl and add the chocolate mixture. Stir until completely combined and the batter is even chocolate.
Alternate adding vanilla and chocolate batter to each pan, evenly distributing batter into each pan. Use a knife to swirl for a marbled appearance.
Bake at 350F (175C) for 30 minutes, or until a toothpick inserted in the centre comes out mostly clean but with a few moist crumbs.
Allow the cake to cool for 15 minutes before carefully inverting it onto a cooling rack to cool completely before serving the cake.
