For High Altitude Instructions, see Notes.
Preheat oven to 350°F. Line a 9x13 inch baking pan with parchment paper, or grease the pan if you don't plan to remove the cake from the pan. Set aside.
Sift together the cake flour, baking powder and salt in a large bowl. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a hand mixer, beat the butter on high speed until light and fluffy (about 1 minute).
Add the granulated and brown sugars to the butter and beat on high speed until pale and fluffy (about 3-4 minutes).
With the mixer running on low speed, add the eggs one at a time until well combined. Next, add the yolks one at a time until fully incorporated. Scrape down the bowl if needed and add the vanilla extract. Beat on medium-high speed until combined.
With the mixer running on low, slowly add in the dry ingredients in 3 portions, alternating with 3 portions of the buttermilk. Mix until just incorporated but do not over mix.
Remove one cup of the yellow cake batter and pour into a medium bowl. In a small pan on the stove over low heat, or in the microwave in 20 second intervals, melt the chocolate. Let cool slightly and fold into the reserved yellow cake batter.
Pour half of the yellow cake batter into the 9x13 inch cake pan. Carefully spread until evened out in the pan if needed.
Next, spoon equal dollops of the chocolate cake batter into the pan. Finish by pouring your remaining yellow cake batter over the top. Don't worry, it doesn't need to be perfect because you are going to swirl!
Take a knife and gently swirl the two batters together.
Bake for 30- 35 minutes, or until a toothpick inserted into the center comes out clean. Just be sure to carefully watch so that it does not overbake. It really depends on your oven!
Remove from oven and cool on a wire rack in the pan. Frost the cooled cake with Dark Chocolate Buttercream or any frosting you would like. Add sprinkles too!