Preheat oven to 350 degrees. Melt chocolate and butter over hot water in a double boiler. Remove from heat and let cool slightly. Beat eggs and sugar in small bowl of electric mixer until very light and lemon colored. Dissolve instant coffee in water and add to egg mixture. Blend at low speed. Fold in flour.
Mix well at low speed. Stir in nuts by hand. Pour into buttered and floured 9-inch square pan. Bake for 20-25 minutes. Frost when cool. Make frosting by melting the 2 ounces of chocolate over a double boiler.
Cream the butter and powdered sugar together. Stir in the chocolate and Kahlua. Spread onto the cooled brownies. Let set in a cool place 30 minutes before serving.