For the cake:
4 whole large eggs
2 egg yolks
2 teaspoons vanilla extract
1 1/4 cups of buttermilk
3 cups cake flour
2 cups sugar
4 1/2 teaspoons baking powder
1/2 teaspoon salt
8 ounces (2 sticks) unsalted butter at room temperature
Preheat the oven to 350 degrees F. Butter the bottom and sides of three 9-inch round cake pans. Line with parchment paper and grease the paper.
Place the eggs and the yolks in a medium bowl. Add the vanilla and 1/4 cup of buttermilk. Whisk to blend well.
Combine the flour, sugar, baking powder, and salt in a large mixer bowl and whisk to blend. Add the remaining buttermilk and butter to the dry ingredients and with the mixer on low speed, blend together. Raise the mixer to medium speed and beat until light fluffy, about 2 minutes.
Add the egg mixture in 3 additions, scraping down the sides of the bowl after each addition. Mix only until thoroughly incorporated. Divide the batter among the prepared pans.
Bake the cake layers for 28-32 minutes or until a toothpick inserted in the center comes out clean. Let the cake layers cool in the pan for 10 minutes, then carefully turn out the cakes onto a wire rack and peel off the paper liners. Cool completely before frosting.
For the frosting:
6 ounces of unsweetened chocolate melted and cooled
4 1/2 cups of confectioners sugar
12 ounces of unsalted butter at room temperature
6 tablespoons of half and half
1 tablespoon of vanilla extract
Place all the ingredients in a food processor and pulse to incorporate. Then, process until frosting is smooth.