How to Make It
Preheat oven to 425°F. Cut pumpkin into quarters; discard seeds. Place on a baking sheet, and drizzle with 2 tablespoons of the olive oil. Bake in preheated oven until tender, 45 minutes to 1 hour. Cool until easy to handle. Remove skin, and discard. Set aside 1 1/2 cups (about 15 ounces) cooked pumpkin; reserve remaining pumpkin for another use.
Heat remaining 2 tablespoons olive oil in a large saucepan over medium. Add onion, celery, carrots, garlic, thyme, sage, and oregano; cook, stirring occasionally, until vegetables are very tender, 8 to 10 minutes. (Do not brown.) Add salt and turmeric; cook, stirring often, 1 minute. Stir in chicken broth and 1 1/2 cups cooked pumpkin; bring to a simmer. Cover and simmer 15 minutes. Remove and discard herb sprigs.
Place half of pumpkin mixture in a blender. Remove center piece of blender lid (to allow steam to escape); secure lid on blender, and place a clean towel over opening in lid. Process until mixture is very smooth, 1 to 2 minutes. Transfer to a large bowl. Repeat procedure with remaining pumpkin mixture. Stir in the apple cider vinegar.
Whisk together sour cream and milk in a small bowl. Divide soup evenly among 6 shallow bowls; drizzle with sour cream mixture, and sprinkle with pomegranate seeds and pumpkin seeds, if desired.