in saucepan, cook sugar and butter over medium heat, stirring occasionally, until sugar is dissolved, about 3 minutes. Add Rum. Without stirring but brushing down side of pan with pastry brush dipped in cold water, cook until amber in colour, 10 to 12 minutes.
whisk in cream and salt; bring to boil. Cook, whisking, until slightly thickened, about 1 minute. Whisk in rum; remove from heat. Let stand until thickened, about 30 minutes.
In a small bowl combine allspice, cinnamon and salt. Pour mixture over the peach halves. Let sit
Place coated peaches on the grill, cook on a medium heat for 3-5 minutes.
Remove peaches from grill. On each plate add a peach halve, top with buttered rum sauce and add a scoop of vanilla ice cream. Add more sauce for taste.