In a large stockpot, add butter on low / medium heat.
Once melted, add cream. Whisk.
Once warmed, add cream cheese (it helps if cream cheese is at room temperature.). Whisk until melted and well incorporated.
Slowly add in parmesan cheese, in batches. Whisk continuously. This process takes a bit of time, but be patient!
Once all cheese is melted, add the milk to thin out. You can add a little more if desired. It thickens considerably in the canner, so you need to thin it out some.