In a thick, uncovered Presto®-style saucepan, preheat the oil over medium heat. Sauté green onions, celery and garlic for 2-3 minutes, stirring constantly.
Add carrots and cabbage and continue to cook for 6-7 minutes. Mix constantly.
Add the broth, water, diced tomatoes, Provencal herbs, celery seeds, salt and pepper and mix well. Cook over medium-low heat for 1 hour 30 minutes or until cabbage reaches desired texture. Mix occasionally.