Begin by warming a footed glass or mug by filling it with hot water, then discard the water. Pour the steaming hot coffee into the preheated glass, filling it about three-quarters full. Stir in the brown sugar until it completely dissolves, creating a smooth, sweet base. Mix in the Irish whiskey, blending the flavors. To finish, gently float a layer of lightly whipped heavy cream over the back of a spoon onto the surface of the drink. Serve immediately while hot, allowing the cream to form a rich collar