Grease two 9-inch pans. Line the bottom with parchment paper. Preheat an oven to 350 degrees F.
In a large mixing bowl, use a hand mixer to cream the butter, vegetable oil, and sugar together until light and fluffy. Add in buttermilk, eggs, and vanilla extract and beat until combined.
Add in flour, baking powder, and salt, and mix until just combined.
Divide the batter among the two prepared pans. Bake at 350 for 25 to 30 minutes, until a toothpick inserted into the center comes out clean.
Let sit in pans for 5 minutes and then transfer to a wire rack to cool completely.
In a large sauce pan, stir together milk and 1/4 cup sugar. Bring to a simmer over medium heat. In a separate mixing bowl, whisk together egg, egg yolks, cornstarch, and 1/3 cup sugar.
Once the milk has reached a simmer, work quickly and carefully pour half of the hot milk in a steady stream into the egg mixture, whisking constantly to avoid curdling or cooking the eggs. Immediately pour the egg mixture back into the saucepan, whisking constantly. Return to a medium heat and whisk constantly until mixture thickens.
Remove from heat once thickened and stir in butter and vanilla until melted. Pour into a clean mixing bowl and cover with plastic wrap, letting the plastic wrap touch the top of the pastry cream to avoid the creation of any film on top. Cool completely in the refrigerator for at least 4 hours.
In a small sauce pan, bring heavy cream to a simmer over medium heat. Place your chopped chocolate into a small mixing bowl. Pour hot cream over chocolate and let stand 1 to 2 minutes. Stir with a rubber spatula until smooth.
Place a wire rack over a baking sheet. The baking sheet will be used to catch any drips from your ganache. Place a pre-cut cake circle onto the wire rack. Lay the bottom cake layer onto the cake circle.
Spread pastry cream over cake to create a filling. Top with remaining cake layer.
Carefully and slowly pour ganache over cake, letting drip down sides.
Transfer cake to the refrigerator and let cool until set, about 1 hour.