Add the eggs and the oil and mix until well combined.
Add the sour cream, and vinegar, and mix until creamy and smooth.
Add ½ of the flour and ½ of the milk, and baking powder and mix it until almost combined.
Add the rest of the flour and milk and mix until just combined and there are no lumps of flour visible.
Divide the mixture in half, add the melted chocolate, and sift the cocoa powder into one-half of the cake mixture and mix until just combined. Don't overmix.
Divide the vanilla cake batter between two 8-inch baking pans. Using a ¼ cup measure, drop scoops of chocolate cake batter over the vanilla batter, distributing it evenly between the pans.
Use a toothpick or a butter knife to make swirls in the batter creating a marbled effect. Don’t overdo it so you don’t get a mixed batter.
Bake in a 180c (350f) preheated oven for about 25-30 minutes (depending on your oven) or until a toothpick inserted into the cake comes out clean with a few moist crumbs.
Allow the cake to cool completely before frosting so the frosting won't melt off the cake.
Make the frosting
Into a saucepan, add the butter, heavy cream, and dark chocolate, and sift the cocoa powder powdered sugar, and kosher salt.
Heat all the ingredients over medium heat mixing constantly until the mixture is smooth and melted.
Strain the mixture into a large bowl or baking pan to speed up the cooling process.
Cover the top with plastic wrap so that the plastic wrap is directly touching the top of the frosting. This will prevent skin from forming.
Let it cool at room temperature for 30 minutes, and then transfer it to the fridge to cool for another 1-2 hours. (depending on the thickness you are looking for)
Remove the frosting from the fridge and give it a mix with a spoon or a spatula.
Assembly
Pipe a small dollop of the frosting on the surface that you will frost on. Lay the first cake layer over the frosting dot.
Top the first cake layer with about ⅓ of the frosting and spread an even layer using a spatula.
Top it with the second cake layer. Frost the cake with the remaining frosting and make a wave pattern using an offset spatula.
Notes
Use room temperature ingredients. It is important that you use room-temperature ingredients like eggs and butter. This step ensures that your mixture mixes into a homogenous mixture and bakes perfectly. you don’t want to place cold batter into the oven.
Use cake strips! Cake strips give you even and perfectly baked cake layers. Click here for the Amazon link.
Don't over swirl. Use a knife or skewer to gently swirl the batters together. Limit yourself to a few figure-eight motions to avoid over-mixing, which can muddy the distinct colors.
Use room temperature ingredients. It is important that you use room-temperature ingredients like eggs and butter. This step ensures that your mixture mixes into a homogenous mixture and bakes perfectly.
Measure your flour correctly! When measuring your flour, avoid scooping it with a measuring cup. Instead, stir the flour with a spoon to create as many air pockets as possible, and spoon it into your measuring cup. Finally, level it with a back of a knife.
Don't cook this frosting on very high heat so the chocolate won't burn. If you are using very high heat, the texture of this frosting will become grainy and not smooth.
Don’t overmix the batter, you don’t want to develop the gluten in the flour. This step ensures you have a moist cake and not a dense and dry cake.
Line your baking pan with parchment paper! This step helps the cake to bake evenly, and it makes sure that your loaf cake will release easily from the pan.
Be patient! I know it’s extremely tempting to frost this cake as it is pulled out of the oven, but let the cake cool for at least 1 hour so it will be firmer and won’t crumble up, and prevent the frosting from melting.