1cupplus 2 tablespoons (9 ounces) unsalted butter, at room temperature and cut into 1-inch cubes
Center a rack in the oven and preheat to 325 (F). Lightly spray an 8 x 4-inch loaf pan with cooking spray and line the bottom and sides with parchment paper, leaving a 2-inch overhang on the pan’s two long sides. Set aside.
Place 4 ounces roughly chopped chocolate and 2 tablespoons Dutch-processed cocoa powder in one of the medium, heatproof bowls. Place the bowl on top of a saucepan filled with few inches of water, but ensuring that the water does not touch the bottom of the bowl. Melt over medium-low heat, using a heatproof rubber spatula to mix occasionally. Once the chocolate is fully melted, transfer the bowl to cool on a wire rack as you work with the other ingredients.
In the bowl of a stand mixer fitted with a paddle attachment, combine 1 3/4 cups flour, 1 cup plus 2 tablespoons sugar, 1 1/4 teaspoons baking powder, and 1 teaspoon salt. Beat on low speed until combined, and add 1 cup plus 2 tablespoons cubed butter, a few pieces at a time. Continue beating for 2 to 3 minutes, or until the mixture resembles a coarse meal. Slowly add half of the liquid mixture (from the previous steps) and increase the mixer speed to medium-high, beating until fluffy, about 1 minute. Reduce the mixer speed to low and slowly add the remainder of the liquid mixture; beat for 30 seconds, until just combined. Scrape down the bottom and sides of the bowl with a rubber spatula, mixing any leftover ingredients stuck into the batter by hand.
Use a digital measuring scale to measure out 10.85 ounces (see baker's notes for volume measurements) of batter into the bowl containing the melted chocolate. Use a rubber spatula to mix until combined, and pour into the prepared loaf pan and smooth its surface with an offset spatula. Set aside.
Use a digital measuring scale to measure out 10.85 ounces of batter into the second medium bowl. Sprinkle the remaining 1 tablespoon Dutch-processed cocoa powder on top of the batter and use a rubber spatula to mix until combined. Pour into the loaf pan on top of the first layer of cake batter. Smooth its surface with an offset spatula. Pour the remaining vanilla cake batter on top of this layer and smooth its surface with an offset spatula.
Bake in the preheated oven for 1 hour and 15 minutes to 1 hour and 30 minutes, or until a skewer inserted into the center of the loaf cake comes out with few crumbs. Check the loaf cake at the 1 hour mark — if the top of the cake is browning too much, cover with a loose sheet of aluminum foil. Cool on a wire rack. Serve warm, or at room temperature. The cake can be kept at room temperature, wrapped tightly in plastic wrap, for up to 3 days.