Mix 2 tablespoons of the milk with the cornstarch in a small bowl until smooth.
Whisk the cream cheese and salt in a medium bowl until smooth.
Combine the remaining whole milk, the cream, sugar, corn syrup, spices, and tea in a 4-quart saucepan, bring the mixture to a rolling boil over medium high heat, and boil for 4 minutes.
Remove from the heat and let the mixture steep for 10 minutes.
Strain the mixture through a fine sieve into a bowl, squeezing as much of the liquid from the tea leaves as possible.
Return the mixture to the pan, heat to a simmer, and gradually whisk in the cornstarch mixture.
Bring the mixture to a boil over medium high heat, and cook until the mixture becomes slightly thick, stirring constantly.
Remove from the heat.
Gradually whisk the hot mixture into the cream cheese until smooth.
Chill the mixture until cold.
Pour the ice cream into an ice cream maker and churn until thick.
Using 2 one-pint containers, pack each container 1/3 full of the ice cream and then spoon 2 tablespoons sweetened condensed milk on top of the layer. Repeat this twice for each container until each is full. Cover with an airtight lid. Freeze until firm.