IN A MEDIUM-SIZE SAUCEPAN, combine the butter, brown sugar, corn syrup and salt and slowly bring the mixture to a boil, over medium-high heat. Boil until the sugar has melted, about 8 minutes. Then boil 2 minutes longer, stirring often with a wooden spoon. Stir in the cream, bringing the mixture back to a boil and continue to let it boil slowly for 2 minutes longer. Pour in the rum, stir to blend, then let the sauce cool and thicken. Store in a covered clean glass jar. If very cold, remove from the refrigerator at least 1 hour before serving.