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Use 9in (23cm) pans that are at least 2 inches (5.1cm) high. To prevent the cakes from sticking, spray the inside of the pans with baking spray. If you prefer to make a single-layer sheet cake, grease a 9in 13in (23cm 33cm) cake pan. Get out a large mixing bowl and put 2 cups (230 g) of cake flour, 2 teaspoons (8 g) of baking powder, and 1/2 teaspoon (2.5 g) of salt into a sifter. Shake the sifter so the dry ingredients fall into the bowl and put the bowl aside. Cake flour has a lower protein content than all-purpose flour. This will make a lighter textured marble cake. Put 1 cup (230 g) of room-temperature unsalted butter into a large mixing bowl and beat it on high speed for 1 minute. Once the butter is smooth, beat in 3/4 cup (150 g) of granulated sugar and 1/2 cup (100 g) of packed light brown sugar. Keep beating on high for 3 to 4 minutes so the mixture becomes light and fluffy. Stop and scrape down the sides of the bowl with a spatula occasionally. If your butter is too cold, it won't combine smoothly with the sugars and you'll see tiny lumps of butter in the mixture. Reduce the mixer speed to low and add 1 whole egg to the creamed butter mixture. Once the egg is incorporated, beat in the remaining 1 whole egg and 4 egg yolks, 1 at a time. Then beat in 1 tablespoon (15ml) of vanilla extract on medium speed. Using room temperature ingredients will ensure that they combine perfectly in the batter. This will trap air so your cake turns out light and fluffy. Turn the mixer back down to low and beat in 1/3 of the dry mixture. Then mix in 13 cup (79ml) of the buttermilk. Add another 1/3 of the dry mixture followed by the remaining 13 cup (79ml) of buttermilk. Finish mixing in the rest of the dry ingredients. The batter will be thick, but there shouldn't be large lumps. It's alright if there are a few small lumps, since it's important not to over mix the batter. Put 4 ounces (113 g) of coarsely chopped bittersweet or semi-sweet chocolate into a microwave-safe bowl. Microwave the chocolate in 20-second increments until it's melted. Then stir in 1 cup (340 g) of the batter and set it aside. This will make the chocolate batter that you'll need to marble the cake. Divide 1/2 of the plain batter between your prepared pans and spread it evenly or pour all of the plain batter into the large pan. Drop large spoonfuls of the chocolate batter onto the plain batter. Then pour the rest of the plain batter over the batter in the pans. Dip a skewer into some of the chocolate batter and drag it through the plain batter in a figure-8 pattern. Do this 2 to 3 more times so there's a marble effect. Ensure that you're not mixing the batters or you won't see a swirl. If you don't have a skewer, use a butter knife. Put the cake pans in the preheated oven and bake the cakes until they begin to pull away from the sides of the pans. Insert a toothpick to see if it comes out without wet crumbs sticking to it. If there's still batter on the toothpick, bake the cakes for a few more minutes and check them again. If you're baking a 9in 13in (23cm 33cm) marble cake, it may take a few more minutes to finish baking. Check the cake once it's baked for 30 minutes. Turn off the oven and take the cakes out. Set them on a wire rack to cool for a few minutes and then turn them out onto the wire rack. Let the cakes cool before you stack and frost them with 3 cups (700 g) of your favorite chocolate frosting. Cover leftover cake and store it at room temperature for up to 2 or 3 days. You can also refrigerate leftover cake for up to 5 days.
Preheat the oven to 350F (177C) and grease 2 round cake pans. Sift the flour, baking powder, and salt. Cream the butter and sugars for 4 to 5 minutes. Mix in the eggs, yolks, and vanilla on low speed. Mix in the dry ingredients alternating with the buttermilk. Melt the chocolate and stir in 1 cup (340 g) of the batter. Spread some plain batter in the pans and top it with chocolate batter. Use a skewer to swirl the batters. Bake the round cakes for 22 to 27 minutes. Remove and cool the marble cake completely.