In another small bowl stir 1/2 cup of the remaining milk into the cornstarch, stirring until the cornstarch is dissolved
In a large heavy saucepan combine the remaining 4 cups milk and the sugar and bring the mixture just to a boil, stirring until the sugar is dissolved.
Stir the cornstarch mixture, whisk it into the milk mixture, and simmer the mixture, whisking, for 2 minutes. Whisk in the espresso mixture.
Let the mixture cool to room temperature, chill it, covered, until it is cold, and freeze it in an ice-cream freezer according to the manufacturer's instructions.
Makes about 1 quart