Preheat oven to 350º F. Prepare two 8-inch round baking pans.
Chop chocolate and melt in a saucepan over medium-low heat. Set aside to cool to room temperature.
Sift flour, cocoa, baking soda, and salt in small bowl.
Whisk brown sugar, butter, eggs, espresso, and vanilla extract for 3 minutes. (Or about a minute with a hand-held mixer or stand mixer)
Gradually add melted chocolate and continue whisking for an additional minute.
Stir flour mixture into creamed mixture and then add buttermilk.
Pour into prepared pans.
Bake for 33 to 38 minutes or until wooden pick inserted in center comes out somewhat clean(not wet). Cool in pans on wire racks for 10 minutes. Run a knife around edges of cakes.
Invert onto wire racks; cool completely.