To begin, preheat the oven to 350º F and prepare two 8-inch round baking pans.
Next, chop the chocolate and melt it in a saucepan over medium-low heat, then set it aside to cool to room temperature.
In a small bowl, sift together the flour, cocoa, baking soda, and salt.
In a separate bowl, whisk together the brown sugar, softened butter, eggs, espresso, and vanilla extract for about 3 minutes.
If using a hand-held mixer or stand mixer, this step should take about 1 minute. Gradually add the melted chocolate and continue whisking for an additional minute.
Stir the flour mixture into the creamed mixture and then add the buttermilk.
Pour the batter into the prepared pans and bake for 33 to 38 minutes, or until a wooden pick inserted in the centre comes out somewhat clean.
Let the cakes cool in the pans on wire racks for 10 minutes, then run a knife around the edges of the cakes and invert them onto wire racks to cool completely.