In a medium size pot over medium heat whisk together the brown sugar, butter and heavy whipping cream until smooth, about 4 to 5 minutes. Remove the pot and stir in the rum. Return to the heat to thicken. Keep warm.
Next brush the pineapple on both sides with butter and grill for 2 to 4 minutes on each side or until browned and tender.
Remove from the grill and top off with ice cream and rum caramel.