In large saucepan, heat oil over medium-high heat. Add onion and cook until golden, about 5 minutes. Stir in broth, broccoli, water, potato, pepper, salt, thyme, and nutmeg. Heat to boiling over high heat. Reduce heat to low, and simmer until potato is cooked, about 15 minutes. Cool 10 minutes.
Puree soup in blender until smooth. Pour back into saucepan. Stir in milk, and warm soup over low heat. Serve with croutons, if desired.