In a very large soup or stock pot, combine all the ingredients - cream, milk, sugar, cream cheese, vanilla and salt.
Cook over medium heat. Stir it occasionally until it is bubbling. Use a whisk to stir and cook for a few minutes, to make sure the sugar is dissolved and the cream cheese is completely melted into the mixture.
Cover and remove from heat. Allow the ice cream mixture to cool for about 30 minutes. Then transfer it into a 4-quart ice cream maker insert. Then allow it to chill in the refrigerator overnight.
Place the filled insert into the ice cream maker. Layer ice and rock salt around the sides until it comes up almost to the top of the lid. I used about 4 cups of salt.
Turn on the ice cream maker and allow it to mix and freeze the ice cream. The ice cream will expand. Also, add more ice as it starts to melt - you want to keep the ice almost to the top of the lid. Mine took about 30 minutes to fully churn and freeze the ice cream.
You can serve the ice cream immediately, but it will be soft. I recommend transferring the ice cream to air tight storage containers. And then allowing the ice cream to continue to firm up in your freezer overnight.