Add the cider, cinnamon, allspice and cloves to a small saucepan, heat to boiling. Reduce heat to moderate level and continue cooking to reduce the apple cider to about half a cup. Fish out the cinnamon stick, allspice berries and cloves and discard.
Stir in the sugar and corn syrup and cook, stirring until sugar is completely dissolved and syrupy. Add the cream and stir to combine. Add one tablespoon of butter stirring until melted then add the second tablespoon of butter and salt. Stir until butter is melted.
Let the sauce cool for 10-15 minutes then stir in the rum to taste. Serve warm or chilled over poached or baked apples or pears, or with ice cream, fruit tarts or any other treat that needs embellishment. Store in a glass or tupperware jar in the refrigerator.