In a small bowl, stir together cornstarch and 1/4 cup of the milk. Set aside.
In a medium-sized saucepan, whisk together remaining 1 1/4 cups milk, heavy whipping cream, lime juice, sugar, corn syrup, and salt.
Bring to a boil on medium-high heat. Continue to boil for four minutes.
Stir in cornstarch slurry and return to a boil. Boil for two minutes.
Pour about 1/4 cup of the milk mixture into a bowl with the cream cheese and whisk until smooth. Add the remainder of the milk mixture and whisk to combine.
Pour into the bowl of a Cuisinart ICE-100 and churn for 60 minutes.
Eat immediately or transfer to a container and place in the freezer if you prefer a harder ice cream.