• Preheat the oven to 350°.
• Line 13 x 9-inch baking pan with nonstick foil.
• Whisk together the eggs and yolks, buttermilk, and vanilla. Set aside.
• Put the flour, sugar, baking powder, baking soda, and salt into the bowl of a stand mixer.
• Whisk the mixture together. Then switch to the paddle attachment.
• Add butter and oil and mix at low speed to combine, then increase the speed and mix until light and fluffy.
• Reduce speed to low and slowly add the egg mixture.
• Once eggs are incorporated, scrape down the bottom of the mixer bowl.
• Beat on medium-high 3 minutes.
• Scrape the batter into the prepared pan and smooth the top.
• Rap pan on counter to tap out air bubbles.
• Bake for 28 to 32 minutes or until a toothpick inserted in the middle comes out with only a few crumbs. Cool completely on a rack.

Frosting

• Beat powdered sugar, cocoa powder, butter and hot water in the bowl of a stand mixer fit with the whisk attachment.
• Mix on low to combine, then increase the speed to medium.
• Mix about a minute until the mixture is smooth. Scrape down the sides of the bowl, mix briefly, then add the chocolate.
• Mix on low until combined, scraping down the sides and bottom of the bowl as needed, then let the frosting sit at room temperature until spreadable, about 30-40 minutes.
• Frost cake, then chill to let the frosting firm up.