Mix about 2 tablespoons of the milk with the cornstarch in a small bowl to make a smooth slurry. Whisk the cream cheese and salt in a medium bowl until smooth. Fill a large bowl with ice and water.
Combine the remaining milk, the cream, sugar, corn syrup, and vanilla seeds and bean in a 4-quart saucepan, bring to a rolling boil over medium-high heat, and boil for 4 minutes. Remove from the heat. Stir the cornstarch slurry and gradually whisk into the milk mixture. Bring the mixture back to a boil over medium-high heat and cook, stirring with a heatproof spatula, until slightly thickened, about 1 minute. Remove from the heat. Makes about 1 quart.
Gradually whisk the hot milk mixture into the cream cheese until smooth. Pour the mixture into a heat-proof 4-cup glass measure or bowl and place in the ice bath. Let stand, adding more ice as necessary, until cold, about 30 minutes, stirring occasionally.
Remove the vanilla bean pieces. Pour the ice cream base into the frozen canister and spin until thick and creamy. Pack the ice cream into a storage container, press a sheet of parchment directly against the surface, and seal with an airtight lid. Freeze in the coldest part of your freezer until firm, at least 4 hours.