1. In a small bowl, whisk together the cornstarch with 2 tbsp. of the milk to create a slurry. Set aside.
2. Whisk together the heavy cream and corn syrup in a pitcher with a spout.
3. Pour the sugar into a tall saucepan over medium-high heat and let the sugar melt and turn brown. Stir with a heat proof spatula as needed to prevent burning.
4. From a distance pour about ¼ cup of the cream mixture into the sugar. It will sizzle and splatter as it hits the sugar. Stir until combined and then continue to add the cream mixture ¼ cup at a time until it has all been combined.
5. Return the saucepan to medium-high heat and add the remaining milk. Bring to a rolling boil and boil for 4 minutes.
6. Meanwhile, mix the cream cheese and salt together in a large bowl until smooth.
7. Remove the saucepan from the heat and slowly whisk in the cornstarch slurry. Place the saucepan back over the heat again and cook, stirring until slightly thickened.
8. Remove from the heat and whisk the caramel/milk mixture into the cream cheese mixture until smooth. Cover and chill for at least 4 hours but preferably overnight.
9. Pour the mixture through a fine mesh strainer, discarding any lumps. Process through an ice cream maker according to directions.