In a medium mixing bowl, stir together condensed milk, peanut butter, vanilla, and salt. Set aside.
In a large, chilled mixing bowl, beat heavy cream on high until soft peaks form.
Beat peanut butter mixture into whipped cream.
Stir in peanut butter cups.
Pour half of the mixture into a 9×5 loaf pan. Drop a few tablespoons of marshmallow cream into the pan and swirl with the ice cream mixture. Repeat this process with second half of ice cream and additional marshmallow cream.
Cover with plastic wrap and freeze for a minimum of 6 hours, preferably overnight.