Preheat your oven to 350°F (175°C). Grease your 9-inch round cake pan with butter or cooking spray and line the bottom with parchment paper for easy release.
In a large mixing bowl, combine 4 large eggs, 2 large egg yolks, 1 cup of buttermilk, and 1 tablespoon of vanilla extract. Whisk until well blended.
In another bowl, whisk together 2 ½ cups of cake flour, 1 ½ cups of sugar, 1 ½ teaspoons of baking powder, ½ teaspoon of baking soda, and ½ teaspoon of table salt until evenly combined.
In a large bowl, beat 8 tablespoons of softened butter with ½ cup of vegetable oil using an electric mixer until light and fluffy.
Gradually add the dry mixture to the butter and oil mixture, alternating with the wet ingredients. Start and end with the dry ingredients, mixing until just combined. Do not overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula. Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes, then transfer to a cooling rack to cool completely.
To make the chocolate frosting, combine ½ cup softened butter, 1/3 cup cocoa powder, and 3 cups powdered sugar in a bowl. Gradually add 1/3 cup milk until desired consistency is reached. Mix until smooth and creamy.
Once the cake is completely cool, place it on a serving platter and spread the chocolate frosting evenly over the top using an offset spatula. Let frosting spill over sides for a rustic look if desired.