Preheat the oven to 350 degrees F (175 degrees C). Line three 8-inch cake pans with parchment paper. Grease the pans and dust with cocoa powder.

Sift together flour, cocoa powder, baking soda, and salt in a bowl. Set aside.

Beat butter, dark brown sugar, and white sugar together in a bowl using an electric mixer until light and fluffy. Add egg yolks one at a time, scraping down the bowl after each addition. Beat on medium-high until fluffy.

Pour melted chocolate and vanilla extract into the bowl with the sugar mixture; mix on low speed until combined. Alternate adding flour mixture and buttermilk, beginning and ending with flour mixture, mixing on low speed. Pour in coffee slowly in a steady stream; mix on low speed until smooth.

Use an electric mixer to beat egg whites in a separate bowl until stiff peaks form. Fold gently into batter. Divide batter evenly between the 3 prepared cake pans.

Bake in the preheated oven until a toothpick inserted into the centers comes out clean, 20 to 25 minutes, making sure not to overbake. Let cool in pans for 10 minutes; turn out onto waxed paper to cool completely before frosting.