Preheat the oven to 350°F and arrange a rack to the center of the oven. Spray a 9x13 baking dish liberally and then flour, tapping out excess. Set aside.

In a medium mixing bowl, whisk together the eggs, yolks, buttermilk and vanilla, approximately 1 minute. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl using an electric hand mixer, combine the flour, sugar, baking powder, baking soda and salt, mixing on low for 30 seconds.

Add the butter and oil, slowly increasing speed and mixing for about 1 minute. Slowly add the liquid mixture while still blending until no dry spots appear. Stop and scrape down the sides and then beat for an additional 3 minutes on medium speed.

Pour into the prepared cake pan, tapping several times to release air bubbles.

Bake for 28-32 minutes or until the cake passes the toothpick test. Cool fully on a wire rack.