Mix milk, cream, and sugar together in a large bowl. Refrigerate to let sugar dissolve.
Meanwhile, brew coffee grounds with water in a coffee maker or French press. Refrigerate coffee until completely cooled, at least 30 minutes.
Beat milk mixture using an electric mixture until slightly thickened to the consistency of buttermilk. Stir coffee into milk mixture.
Pour mixture into an ice cream maker and freeze according to manufacturer’s instructions, 20 to 30 minutes. Serve or transfer to an airtight container and store in the freezer.