Ensure your ice cream maker bowl is completely chilled (at least 12 hours in the freezer).
In a saucepan, heat heavy cream just enough to dissolve the cream cheese, creating a smooth, lump-free mixture. Allow to cool completely.
In a large bowl, combine sweetened condensed milk, evaporated milk, cream cheese mixture, and salt. Chill in the refrigerator for at least 2 hours to let flavors meld.
Pour mixture into ice cream maker bowl and churn according to manufacturer instructions until soft-serve consistency is reached (approx. 30 minutes).
Transfer ice cream to an airtight container using a rubber spatula. Cover and freeze for 2–3 hours until firm, then serve.