Preheat the oven to 340°F (170°C). Grease two 8-inch round cake pans and line the bottoms with parchment paper.
In a small bowl, whisk together the Dutch-process cocoa powder and 3 tablespoons of hot coffee until completely smooth. Set aside.
1/3 cup Dutch-process cocoa powder, 3 tablespoons hot coffee
In a large bowl, whisk together the flour, granulated sugar, baking powder, and salt.
2 1/3 cups all-purpose flour, 1 1/2 cups granulated sugar, 1 tablespoon baking powder, 3/4 teaspoon salt
In a separate bowl, whisk the eggs, sour cream, vegetable oil, melted butter, vanilla extract, and whole milk until smooth.
3 large eggs, 1 cup sour cream, 1/2 cup vegetable oil, 1/4 cup unsalted butter, 2 teaspoons vanilla extract, 1/2 cup whole milk
Pour the wet ingredients into the dry ingredients and stir until just combined.
Transfer about 1/3 of the batter (roughly 1 1/2 cups) to a separate bowl. Add the bloomed cocoa paste, 2 tablespoons of granulated sugar, and 1 tablespoon of vegetable oil. Fold until uniform.
2 tablespoons granulated sugar, 1 tablespoon vegetable oil
Divide the vanilla batter between the two pans. Dollop the chocolate batter on top (5-6 spoonfuls per pan). Swirl with a knife 3-4 times.
Bake for 27-32 minutes, until a toothpick comes out with moist crumbs. Cool in pans 10 minutes, then turn out onto a wire rack to cool completely.