1. Place three cups of the cooking liquid into a pot (discard any remaining liquid) and add remaining ingredients, except cornstarch. Let simmer over medium-low heat until reduced, and ingredients are fully combined, about 15 minutes. Add the dissolved cornstarch and mix well to incorporate. Cook about five more minutes until sauce begins to thicken (it will thicken more as it cools).
2. Pour sauce over sliced meat and freeze, or reheat for half an hour before serving. Garnish with chopped parsley.