Fill a large bowl with ice water. In a small bowl, mix 2 tablespoons of the milk with the cornstarch. In another large bowl, whisk the cream cheese until smooth.
In a large saucepan, combine the remaining milk with the heavy cream, sugar and corn syrup. Bring the milk mixture to a boil and cook over moderate heat until the sugar dissolves, about 4 minutes. Off the heat, gradually whisk in the cornstarch mixture. Return to a boil and cook over moderately high heat until the mixture is slightly thickened, about 1 minute.
Gradually whisk the hot milk mixture into the cream cheese until smooth. Add the chopped mint. Whisk in the salt. Set the bowl in the ice water bath and let stand, stirring occasionally, until cold, about 20 minutes.
Strain the ice cream base into an ice cream maker, pressing the mint leaves with the back of a spoon to extract all of the flavor, and freeze according to the manufacturer's instructions. Pack the ice cream into a plastic container.
Press a sheet of plastic wrap directly onto the surface of the ice cream and close with an airtight lid. Freeze the mint ice cream until firm, about 4 hours.