Freeze bowl: Approximately 18 hours ahead of time: Place the ice cream bowl in the freezer. Make sure the freezer is set to 0 degrees or colder.
Prep for the ice cream base: 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.
Cook: Combine the remaining milk, the cream, sugar, corn syrup in a 4-quart saucepan, bring to a rolling boil over medium-high heat, and boil for 4 minutes -- watch it closely and stir occasionally to make sure it doesn't boil over.
Steep: Remove from the heat, stir in thai tea and let sit for 5 minutes. Then strain mixture over a mesh strainer. (It is okay if a few black tea pieces remain)
Thicken: Gradually whisk the cornstarch slurry into the strained 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.
Chill: Gradually whisk the hot milk mixture into the cream cheese until smooth. Pour the mixture into a 1-gallon Ziploc freezer bag and submerge the sealed bag in the ice bath. Place in fridge for 30 minutes to an hour until cold.
Freeze: Pour the ice cream mixture into the frozen canister and turn on the machine. Spin the ice cream until thick and creamy.
Pack the ice cream into a storage container, and seal with an airtight lid. Freeze in the coldest part of your freezer until firm, about 4 hours.