Place peas, green onion, thyme, sugar and broth in medium saucepan. Bring to a boil, reduce heat, cover and simmer 10 minutes. Let mixture cool slightly. Puree, in batches, in food processor or blender.
Stir in milk, season with salt and pepper. Cover and refrigerate 4 hours or overnight. Garnish servings with freshly grated nutmeg and shredded carrot.