In a 5-quart Dutch oven or saucepot heat oil over low heat. Add chopped green onions (white part only); saute until browned, about 2 minutes.
Add peeled, seeded, and diced butternut squash, water, and thyme. Cover and simmer for 10 to 15 minutes or till squash is tender.
Stir in flour. Cook for 1 minute. Add chicken broth; bringing to a boil. Reduce the heat and simmer, uncovered, for 10 minutes. Remove from the heat and stir in milk.
In a blender or food processor, blend squash mixture at low speed in batches until smooth. Serve soup with sprinkled nutmeg.