1. Whisk 2 tablespoons of the eggnog with cornstarch in a small ramekin and set aside.  In a separate bowl whisk the cream cheese and salt until smooth. Finally, fill a third bowl with ice and set aside.

2. Pour the remaining eggnog into a large saucepan and add the cream, sugar, and corn syrup. Whisk continuously and bring to a boil over medium heat. Allow to boil for four minutes. Remove the mixture from the heat and whisk in the cornstarch slurry, then place the pan back on the burner. Boil for one more minute, stirring the whole time until the mixture thickens and coats the back of a spoon. Remove from heat.

3. Slowly pour the warm mixture into the bowl with the cream cheese and whisk until completely smooth. Then stir in the dark rum. Pour the mixture into a large ziploc bag and submerge the sealed bag in the bowl of ice to chill for at least 30 minutes.

4. Pour the mixture into the ice cream mixer and churn according to manufacturers directions. Press the ice cream into a container and freeze.