The Directions To Follow:
Heat oven to 350 degrees. Prepare two 8-inch round cake pans by adding a piece of parchment to the bottom of the pan.
Sift together cake flour, baking powder and salt in a medium bowl and set aside.
In the bowl of a stand mixer with whisk attachment cream together butter and sugar on medium-high until light and fluffy.
With the mixer on low, add in milk and vanilla and fully incorporate. (usually about 1 minute)
In a small bowl add the melted butter and cocoa and mix until combined.
Add 3/4 cup of the yellow cake batter into the cocoa/butter mixture and fold together.
Now add 3/4 cup of yellow cake batter to each cake pan and smooth out.
Divide the chocolate batter evenly between the two pans by dropping spoonfuls in a circle over the yellow batter.
Divide the remaining yellow cake batter between the pans and smooth out as much as possible without mixing.
Take a clean table knife and make a swirling patter throughout the cake to gently achieve the marble effect.
Bake for 20-30* minutes.
How to make the frosting:
In a the bowl of an electric stand mixer, fitted with whisk attachment whisk butter and sugar on medium-high speed until very pale and fluffy or about five minutes.
Once all cream has been added and mixture is mostly combined, turn off the mixer and scrape down the sides of the bowl.
How to put it all together:
Place one layer of cooled marble layer on cake stand. (You should not have needed to level these cakes, but in the small change that you did now would be the time to do so.)
Cover in about 1/2 cup (can use more if desired) of chocolate buttercream and smooth out with an offset spatula.
Gently set other marble cake layer on top and make sure it is centered.
Starting with about 1 cup of chocolate buttercream scooped on top of the cake, start to smooth the frosting out and over the sides of the cake. There is enough frosting to covered this entire cake with a little left over, so feel free to use a healthy amount of cover sides.
Once cake is covered in frosting use a butter knife or offset spatula to create the letter “C” or swoops in the frosting.
Best served at room temperature, but you can also chill until ready to serve.
Source: IAmBaker.com