In a large bowl, whisk together sweetened condensed milk, coconut oil, rum and salt. In a separate bowl, beat cream on high until stiff peaks form, about 1 1/2 minutes.
Whisk half the cream into milk mixture. Fold in remaining cream. Transfer to a 4 1/2-by 8 1/2-inch loaf pan. Freeze until firm, at least 6 hours, and up to 1 week.