In a medium pot, combine the milk/corn starch mixture, the butter, the mozzarella and the parmesan. Bring to a boil, over medium high heat, stirring constantly, until the cheese melts and the mixture thickens, about 5 minutes.
Transfer to the blender and add one cup of heavy cream. Blend until smooth, adding more heavy cream as necessary for a consistency similar to sweet condensed milk.
Taste for seasoning and add salt if necessary.
Use immediately or refrigerate for up to a week.
Notes
You can freeze the cream cheese for up to 3 months. If the cream cheese thickens too much after a few days in the fridge, pop it in the blender with a few splashes of heavy cream until smooth.