In a large, non-stick skillet, add the olive oil, onions, garlic, and celery. Add the chicken broth, Vermouth, bay leaf, salt, and pepper, and bring to a boil. Reduce the heat to low and cover. Simmer, turning once, until the celery is tender, about 30 minutes.
Remove from the heat and transfer the celery to serving plates. Spoon a little cooking liquid over each serving, and sprinkle with the parsley and toasted walnuts. Serve.
Yield: 4 servings