Heat the chocolate and coffee together over low heat using a double boiler or large heatproof bowl set over a saucepan of shallow water. Stir occasionally with a long wooden spoon until the chocolate is just melted. Immediately remove heat and stir again until velvety smooth.
Take the bowl of melted chocolate off the pan of hot water. With an electric mixer or whisk, beat the butter into the chocolate one tablespoon at a time.
Submerge the bottom quarter of the bowl in icy cold water and beat the frosting at medium-high speed until of good spreading consistency. (After about 5 minutes it will lighten in color, signaling that it will be ready quickly.)
Use immediately. Serve at room temperature.
Note
Storing - Can be stored at room temperature for a few days, covered and kept away from sunlight and heat, or kept in an airtight container in the refrigerator for up to a week, and in the freezer for up to a month. Let come to room temperature before using. Whip, whisk or stir to restore a smooth, fluffy texture.