In a mixing bowl, whisk together the milk, heavy cream, sugar, cooled coffee, and vanilla extract until the sugar dissolves.

Pour the mixture into an ice cream maker and churn according to the manufacturer’s instructions.

If you don’t have an ice cream maker, pour the mixture into a shallow dish and freeze for 1 hour. Stir vigorously to break up ice crystals, then return to the freezer. Repeat this process every 30 minutes for 4 hours until creamy and frozen.

Scoop the ice cream into small cups or bowls.

Pour a shot of hot espresso over the ice cream just before serving for the classic affogato experience.