Bring 3 quarts of water to boil in a heavy pot. Squeeze the flesh out of the garlic heads into the pot. Add the artichokes, celery root, olive oil, rosemary, thyme, saffron, turmeric and salt to taste. Bring back to boil, then reduce to medium. Cook, covered, 30 minutes. Puree the soup with an immersion blender. Add ground pepper to taste and chives. Adjust consistency and seasonings. Serve hot. Delicious chilled too.