In the bowl of a food processor, combine all of the ingredients except the milk and process until the sugar is dissolved, approximately 1 minute. Transfer the mixture to a mixing bowl and whisk in the milk. Cover the bowl and place in the refrigerator until the mixture reaches 40ºF or below, approximately 1 hour.
Pour the mixture into an ice cream maker and process according to the manufacturer's instructions until it is the consistency of soft serve ice cream, 25 to 35 minutes. Serve as is or transfer to a lidded container and place in freezer until firm, approximately 3 hours.