Irish Mocha Frost

In a small saucepan, combine coffee, milk and cocoa. Heat the mixture over moderate heat, whisking, until the cocoa is dissolved, and let it cool. Stir in 1/2 cup of the liqueur, pour the mixture into a metal ice tray fitted with the divider, and freeze it until it is frozen solid. The coffee mixture may be prepared up to this point 1 day in advance. In a blender, blend the frozen coffee mixture with the remaining 1/2 cup liqueur, scraping down the sides occasionally, until the mixture is smooth but still frozen and divide the mixture between 2 stemmed glasses.