Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a saucepan over low heat, combine the finely chopped unsweetened chocolate and half-and-half. Stir until completely melted and smooth. Remove from heat and let it cool slightly.
In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, light brown sugar, baking powder, baking soda, salt, and Dutch-processed cocoa powder until well combined.
In another bowl, mix together the brewed coffee, buttermilk, and 2 teaspoons of vanilla extract.
In the bowl of your stand mixer, beat the unsalted butter until creamy. Gradually add the dry ingredients, alternating with the wet mixture, and then mix in the melted chocolate. Beat until just combined.
Add the eggs to the batter one at a time, mixing well after each addition. Scrape down the sides of the bowl as needed.
Divide the batter evenly between the prepared cake pans. Bake for 30-35 minutes or until a toothpick inserted in the center comes out clean. Let the cakes cool in the pans for 10 minutes before transferring them to a cooling rack.
While the cake layers are cooling, prepare the frosting. In a saucepan, heat the remaining half-and-half and the chopped chocolate until melted and smooth. Remove from heat and let it cool slightly.
Once the cakes are completely cooled, place one layer on a serving plate. Spread a generous amount of frosting on top, then place the second layer on top. Frost the top and sides of the cake with the remaining frosting.
Slice the cake into generous portions and serve it up to family and friends.