Preheat the oven to 350°F (175°C). Grease a 9-inch round cake pan with the softened butter. Line the bottom with a round of parchment paper, butter the parchment, then grease the sides. In a small bowl combine 2 tablespoons flour and 2 tablespoons cocoa powder, and dust the prepared pan with this mixture, tapping out and saving the excess for reuse.

In a medium bowl whisk together 2 cups flour, 1/4 cup unsweetened cocoa powder, 1/2 cup of the granulated sugar, 1/2 teaspoon baking powder, 1/2 teaspoon baking soda, and 1/2 teaspoon salt. Set the dry mixture aside.

Place the 2 eggs (room temperature), 1/3 cup dark brown sugar, and the remaining 1/2 cup plus 1 tablespoon granulated sugar in the bowl of a stand mixer fitted with the whisk (or use a hand mixer). Beat at medium-high speed until the mixture is thick, pale, and increased noticeably in volume, about 5 minutes. Scrape down the bowl as needed.

With the mixer at medium speed, slowly add 1/2 cup of the vegetable oil and beat for about 3 minutes until the oil is absorbed and the mixture is smooth.

Melt the 2 1/2 ounces bittersweet chocolate in a heatproof bowl (microwave in short bursts, stirring between, or use a double boiler) and let it cool slightly. Add the melted chocolate to the mixer bowl and beat briefly to combine.

Slowly add the remaining 1/2 cup vegetable oil to the batter while mixing at medium speed until evenly incorporated. Scrape the sides and bottom of the bowl so the batter is uniform.

In a separate small bowl or measuring cup whisk together 1 cup buttermilk, your chosen amount of instant coffee (use 1 1/2 teaspoons for a subtle coffee note or up to 3 teaspoons for a stronger mocha flavor), and 2 teaspoons vanilla extract.

Reduce the mixer to low speed and slowly beat the buttermilk mixture into the batter until just combined. Stop the mixer.

Using a rubber spatula, gently fold the reserved dry ingredients into the batter in three additions. Fold just until no streaks of flour remain—do not overmix.

Pour the batter into the prepared cake pan and smooth the top. Bake on the middle rack for about 50–60 minutes, or until a toothpick inserted into the center comes out with only a few moist crumbs attached.

Remove the cake from the oven and let it cool in the pan on a wire rack for 10 minutes. Then run a knife around the edge, invert the cake onto the rack, peel off the parchment, and let the cake cool completely before slicing or decorating.

Note: The ingredient list does not include additional items needed to make the frosting described in the original directions, so no frosting instructions are provided here. If you wish to frost the cooled cake, use a frosting recipe that lists its own ingredients.