In a large bowl, beat the cream cheese and sea salt together until well blended. Set aside.
Reserve 2 tablespoons of the milk in a small separate bowl.
In a medium saucepan combine the sugar, remainder of the milk and heavy cream.
Split the vanilla bean in half lengthwise and use a sharp knife to scrape out the seeds. Add the vanilla seeds and the vanilla bean pod to the cream mixture.
Transfer the pot to the stovetop and bring to a boil over medium high heat, stirring often.
While the cream mixture is heating, add the cornstarch to the bowl with the reserved milk and whisk together to form a slurry.
When the cream comes to a boil, set your timer for 4 minutes and continue to cook the mixture at a boil, stirring constantly. Whisk in the cornstarch mixture and boil and stir for one minute. Remove from heat.
Use a pair of tongs to remove the vanilla bean pod and discard. (note: you may want to strain the custard through a mesh strainer if the vanilla pod has fragmented into smaller pieces that are tougher to fish out with tongs - ask me how I know that).
Add 1/2 cup of the cooked custard to the cream cheese mixture and using a hand mixer or whisk, beat until smooth, scraping down the sides of the bowl with a rubber spatula. Add the remainder of the custard and beat until smooth.
Stir the rum into the vanilla custard and let cool to room temperature. Cover and refrigerate for at least 4 hours or overnight. Note: if you have an ice cream maker that requires a frozen canister, it needs to be chilled in the freezer for 24 hours before making the ice cream, so if you haven't done that yet, freeze it now and let the ice cream base chill until the next day.
TO CHURN THE ICE CREAM:
Set up your ice cream maker according to the manufacturer's instrucitons. Add the base to the churn and start the machine. Churn the ice cream until it's thick, frozen and starts to come away from the sides of the ice cream maker. Usually 20-25 minutes, depending on your machine.
ASSEMBLING THE DULCE RUM ICE CREAM:
Choose an ice cream container that will hold a quart of ice cream. You can use a loaf pan or other sturdy plastic based container. Spoon about 1/2 cup of cold dulce de leche into the bottom of the container, followed by a large spoonful of the ice cream. Alternate the layers between ice cream and dulche de leche, finishing with the dulce.
Transfer the ice cream to the freezer and chill until firm, about 4 hours.