Peel peaches but do not remove the stones. Put them in a saucepan with the sugar and water, and cinnamon, to taste. Simmer them, covered, for about 15 minutes. Add Burgundy and continue to cook, uncovered, over a low heat for 15 minutes.
Put peaches in a deep serving dish. Cook the liquid until reduced to the consistency of a light syrup. Pour syrup over the peaches and put in the refri