Preheat oven to 350°F (180°C). Line two 9-inch round cake pans with parchment paper. Butter pans well and dust with cocoa powder, shaking out excess.
Combine coffee and chopped chocolate in a large glass bowl and microwave at high for 1 to 2 minutes or until piping hot and chocolate is melted. Whisk in rum until smooth. Let cool to room temperature.
Place sour cream in a bowl and stir in baking soda and salt.
Cream butter and sugar in a large bowl using an electric mixer until fluffy. Beat in eggs, one at a time, until incorporated. Beat in chocolate mixture until smooth. Beat in half the flour alternately with half the sour cream mixture, beat in remaining flour and sour cream mixture to make a smooth batter. Spread evenly in prepared pans.
Bake on rack in middle of oven for 35 to 40 minutes or until cake feels firm in the centre and edges begin to pull away from sides. Leave in pans for 5 minutes, then turn out onto wire racks to cool. Cake layers can be wrapped well in plastic wrap, then foil and frozen for up to 1 month.
For frosting, sift icing sugar and cocoa powder together through a fine sieve into a large bowl. Beat in butter and rum using an electric mixer, starting at a slow speed, until smooth. Beat in enough sour cream to make a smooth spreadable frosting.
Arrange one cake layer on a large plate and spread with some of the frosting. Top with second cake and spread tops and sides with remaining frosting.