Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x9 inch square pan.

In a double boiler, or in the microwave, melt 5 squares of unsweetened chocolate with 2/3 cup butter. Combine hot water and instant coffee, stir into the melted chocolate. Set aside to cool.

In a medium bowl, beat in eggs, egg yolks, and 1 cup sugar until smooth. Stir in vanilla. Sift together flour, baking powder, and cocoa; mix into the egg mixture. Next, mix in the cooled chocolate mixture. Stir in 1/2 cup walnuts. Spread the batter into the prepared pan.

Bake for 30 to 35 minutes in the preheated oven. Cool completely before frosting.

To make the frosting, melt the remaining 3 squares of unsweetened chocolate in a double boiler. Stir in sour milk, and 1 tablespoon sugar; stir until smooth. Remove from heat, and stir in the rum. Spread over the cooled brownies, and sprinkle with remaining walnuts. Allow the frosting to set before cutting into bars.