Pre-heat oven to 350 F. Cut the squash in half and scoop out the seeds. Place cut side down in baking pan along with a half cup water. Bake for 45 minutes or until tender. Remove from oven. Let cool for a few minutes and remove the flesh from the skin.
Pre-heat olive oil n a 5 quart saucepan. Add onion and saute for 5 minutes or until translucent. Add the celery, garlic, parsley, balsamic vinegar, dried basil and fennel seeds. Cook for a further 5 minutes.
Add vegetable stock, bring to a boil, reduce heat and simmer for 15 minutes, stirring frequently.
Puree the soup in a blender or with an immersion blender, until smooth. Return to heat, taste and adjust salt and pepper to taste.
To serve, drizzle with olive oil, garnish with basil and Parmesan.