Preheat your oven to 350°.
Coat a 9-inch round cake pan with softened butter, then dust with a mixture of flour and cocoa powder, tapping out the excess to reuse. Line the bottom with parchment paper and butter and coat as well.
In a large bowl, whisk together the flour, cocoa powder, ½ cup of the granulated sugar, baking powder, baking soda, and salt. Set aside.
Using a stand mixer fitted with the whisk attachment, beat the eggs with the dark brown sugar and the remaining ½ cup plus 1 tablespoon of granulated sugar at medium-high speed until thick, about 5 minutes. Scrape down the sides of the bowl as needed.
At medium speed, gradually add ½ cup of the vegetable oil and beat for 3 minutes until absorbed. Beat in the melted bittersweet chocolate, then slowly add the rest of the oil until thoroughly blended, scraping the side and bottom of the bowl. You are emulsifying the oil into the batter, like when making mayonnaise or salad dressing.
In a separate bowl, whisk together the instant coffee and vanilla into the buttermilk. Then, at low speed, beat in the buttermilk. Remove the bowl from the mixer and gently fold in the dry ingredients in three additions using a rubber spatula.
Pour the cake batter into the prepared pan and bake for about 50 to 60 minutes, until a toothpick inserted in the center comes out with only a few moist crumbs.
Cool the cake in the pan for 10 minutes, then remove from the pans to a rack to finish cooling. Peel off the parchment paper.
To make the frosting, whisk together the granulated sugar, egg whites, and salt in a medium heatproof bowl. Set over simmering water and whisk gently until the sugar is completely dissolved, about 5 minutes.
Transfer the egg white mixture to the bowl of a stand mixer fitted with the whisk. Add vanilla and beat at medium-high speed until stiff and glossy, about 8 minutes.
Beat in the butter a few pieces at a time, ensuring it is fully incorporated before adding more. If the mixture appears runny, place it in the refrigerator to thicken up, then continue.
Beat in the melted chocolate until fully incorporated, scraping down the bowl as needed. Chill the frosting until needed. If it gets too firm to spread, let it warm up at room temperature.
Set the cake on a platter. Frost the cake with the buttercream. Refrigerate the cake until the frosting is firm.