Place cabbage in large bowl. Pour enough boiling water over to cover. Let stand 5 minutes. Drain well. Pat dry with paper towels. Cut cabbage into thin shreds.
Melt butter in heavy large saucepan over low heat. Add onion; sauté until tender but not brown, about 10 minutes. Add cabbage and potato, stir 5 minutes.
Stir in mace. Add flour, stir 2 minutes. Gradually mix in milk and broth. Bring mixture to boil, stirring frequently. Reduce heat to medium-low and simmer until vegetables are tender, about 20 minutes. Cool slightly.
Puree soup in batches in blender until smooth. Return soup to same saucepan. Season with salt and pepper.
Bring soup to simmer. Ladle into bowls. Sprinkle with parsley, chives and Parmesan and serve.