Preheat oven to 325 degrees. Butter a 9-by-5-inch loaf pan. In a large bowl, whisk together eggs, milk, and vanilla. In another bowl, beat together sugar, flour, baking powder, and salt on low speed. Continue beating while adding butter until mixture is crumbly. Add half of milk mixture; beat on medium-high until fluffy, 1 minute. Add remaining milk mixture and beat until incorporated, about 30 seconds.

In another large bowl, whisk 2 tablespoons cocoa into chocolate. Stir in 1 1/2 cups (285 grams) batter. Spoon into prepared pan, smoothing top with a small offset spatula. Whisk remaining 1 tablespoon cocoa into another 1 1/2 cups (285 grams) batter in bowl; spoon over dark-chocolate layer and smooth top. Spoon in remaining batter; smooth top.

Bake until a tester inserted in center comes out clean, about 1 hour, 30 minutes (if top is browning too quickly, tent with foil). Let cool in pan 15 minutes. Turn out onto a wire rack and let cool completely, about 2 hours.