Preheat oven to 375°.Place the whole acorn squash in a baking dish and bake for 1 hour. Remove from oven, cut open and allow to cool for 5 to 10 minutes. Scoop out seeds, remove skin and set aside.
Heat oil in a soup pot. Add rinsed and chopped leeks and celery and cook on medium heat until translucent—about 5 minutes.
Add baked squash, vinegar and spices. Stir well. Add water, bring to a boil, reduce to simmer and cook for 15 minutes or more. Leave the lid slightly askew so that some of the steam escapes and the soup reduces to a thicker stew.
Garnish with freshly chopped parsley and unsweetened yogurt if you like.