Preheat oven to 325°F. Butter two round cake pans (I used 8 inch) generously, then dust with cocoa powder, knocking out excess.
Heat coffee, buttermilk, rum, butter, and cocoa powder in a medium heavy saucepan over moderate heat, whisking, until butter is melted. Remove from heat, then add sugar and whisk until dissolved, about 1 minute. Transfer mixture to a large bowl and cool 5 minutes.
While chocolate mixture cools, whisk together flour, baking soda, and salt in a bowl. Whisk together eggs and vanilla in a small bowl, then whisk egg mixture into cooled chocolate mixture until combined well. Add flour mixture and whisk until just combined (batter will be thin and bubbly).
Pour batter into pans and bake until a wooden pick or skewer inserted in center comes out clean, 50 to 60 minutes.
Cool cake completely in pans on a rack, about 2 hours. Loosen cake from pans using tip of a thin knife, then invert rack over pan and turn cake out onto rack.