Stir together the coffee and 1 cup of milk in a saucepan over medium flame until a full boil is reached, remove from the heat, and leave to infuse until tepid. Strain through a sieve lined with a cloth, pressing and twisting the cloth to extract as much milk as possible.
Combine all the ingredients, whisk thoroughly, and cook in a bain-marie on top of the stove, the water kept just below the boiling point—or, if you are using a heavy copper saucepan, the custard may be cooked directly over a tiny flame. Stir constantly with a wooden spoon and remove from the heat as soon as the mixture is the consistency of a heavy sauce, coating the spoon easily—it must not approach the boiling point. Pour into ramekins or into a single deep serving dish and chill.