Step 1: Preheat the Oven

1. Preheat your oven to 350°F (175°C).
2. Grease and lightly flour a 9×5-inch loaf pan or line it with parchment paper.

Step 2: Prepare the Batter

1. In a large mixing bowl, cream together the softened butter and sugar using an electric mixer until light and fluffy (about 3–4 minutes).
2. Add the eggs, one at a time, mixing well after each addition to incorporate fully.
3. Mix in the vanilla extract and sour cream until well combined.

Step 3: Combine Dry Ingredients

1. In a separate bowl, sift together the flour, salt, and baking powder.
2. Gradually add the dry ingredients to the wet mixture, mixing on low speed just until combined. Be careful not to overmix, as this can make the cake dense.

Step 4: Separate and Prepare the Chocolate Batter

1. Divide the batter evenly between two bowls.
2. In one of the bowls, add the cocoa powder and warm milk, mixing until well combined. This will create the chocolate portion of the batter.

Step 5: Create the Marble Swirl

1. Alternate dollops of vanilla and chocolate batter into the prepared loaf pan. Begin with a layer of vanilla batter, then add spoonfuls of chocolate batter on top.
2. Use a butter knife to gently swirl the two batters together, creating a marbled effect. Be careful not to over-swirl, as you want distinct chocolate and vanilla streaks.

Step 6: Bake the Cake

1. Place the loaf pan in the preheated oven and bake for 50–60 minutes, or until a toothpick inserted into the center comes out clean.
2. Remove the cake from the oven and let it cool in the pan for about 10 minutes. Then, transfer it to a wire rack to cool completely.

Step 7: Prepare the Vanilla Icing

1. In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth and slightly thick. Adjust the milk to achieve the desired consistency; it should be pourable but not too runny.

Step 8: Ice the Cake

1. Once the cake is fully cooled, drizzle the vanilla icing evenly over the top. Let the icing set for a few minutes before slicing and serving.