In a medium saucepan, combine the heavy cream, milk, and sugar.
Heat the mixture over medium heat, stirring frequently, until the sugar has dissolved and the mixture is steaming.
Remove the saucepan from the heat and stir in the espresso powder and vanilla extract.
Pour the mixture into a shallow baking dish and place in the freezer.
Stir the mixture every 30 minutes for the first 2 hours, then every hour until completely frozen, about 4-6 hours total.
Scoop and serve the coffee ice cream.
