Heat oil in soup pot. Add leeks, onions, and celery. Sauté until limp (about 15 minutes).
Add tarragon, thyme, salt, and pepper. Stir well.
Add chicken broth, potatoes, and carrots. Bring to a boil, reduce heat, cover, and simmer 15 minutes.
Add cabbage and half of spinach. Simmer 1 minute. Remove from heat.
Purée half of soup in blender. Return to pot.
Add milk and remaining spinach. Heat until hot but not boiling. Adjust seasoning. Serve.
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