Cover the apricots with the apple juice and bring to a full boil. Reduce the heat and simmer, covered, 30 minutes. Stir the apricots occasionally so they will not stick or burn. Let the apricots cool, then strain. Reserve the cooking liquid. Chop the cooked apricots and set aside. In a 2-quart saucepan combine the orange juice, honey, water, cornstarch, ginger and cinnamon. Heat, stirring constantly, until thickened slightly. Remove the pan from the heat and add the apricots, their cooking liquid and vermouth. Serve hot or well chilled.