Whisk the cornstarch, sugar, cinnamon and salt in a 2-quart heavy saucepan. Gradually whisk in the milk. Boil the mixture over medium-high heat, whisking constantly, about 2 minutes. The mixture will be thick when done. Remove the saucepan from the heat. Whisk in the espresso and vanilla until smooth.
Transfer the mixture to a bowl and cover with plastic wrap. Chill the bowl in the fridge until cold, at least 2 hours. Serve the pudding chilled.