Make the cupcakes: Preheat oven to 325° F. Line a cupcake pan with cupcake liners, set aside.
In a medium bowl, whisk the flour, baking powder, baking soda, and salt. Set aside.
In the bowl of a stand mixture fitted with a paddle attachment, cream together the butter and sugars. Add the oil and vanilla and mix. Add the egg and egg yolk and mix to combine.
With the mixture on low speed, add half of the flour mixture, all of the buttermilk, then the rest of the flour mixture. Mix until partially combined, then fold in the chocolate chips but don’t overmix.
Fill the cupcake cavities half to 2/3's full, using approximately 3 T of batter in each compartment.
Bake for 17-20 min, or until a toothpick inserted into the middle come out clean or with a couple crumbs stuck to it. Remove from oven, let cool in pan for 5 mins then turn out to cool on a wire rack until room temperature.
Make the chocolate buttercream: Melt the chocolate in a microwave safe bowl at half power, stirring every 30 seconds until smooth. Set aside to cool for 5 minutes. (You don't want to add hot melted chocolate to the butter because it'll melt it and/or make it VERY soft).
In the bowl of a stand mixer fitted with the paddle attachment, whip the butter on medium high speed for 2-3 minutes. Reduce speed to medium and slowly add the powdered sugar. Once the powdered sugar is mixed in, add the vanilla. Beat for 30 seconds.
Pour in the melted chocolate and beat on medium high speed for 2 minutes or until light and fluffy, making sure to scrape down the sides of the bowl so that everything is evenly incorporated. Add the heavy cream (if needed) and beat for another minute.
Place frosting in a piping bag and pipe a generous amount of frosting overtop of each cupcake. Enjoy!