Preheat oven to 350° F and butter and sugar a 9 x 13-inch pan. Whisk water, cocoa powder and chocolate over low heat until chocolate is melted. Allow to cool to room temperature. Combine sour cream, vanilla and peppermint extract and whisk into cooled chocolate mixture. Cream butter and sugars together until fluffy and pale. Add eggs, one at a time, beating well after each addition. Sift together flour, baking soda and salt and add to butter mixture alternately with chocolate mixture. Scrape and spread into prepared pan and bake for 50 to 60 minutes, until a tester inserted in the centre of the cake comes out clean. Allow to cool.
While cake is cooling, prepare frosting. Heat butter, cocoa and milk together until smooth and shiny. Remove from heat and stir in icing sugar and vanilla, and beat until smooth. Pour and spread over cake and allow to cool.