Melt butter in a large pot. Add chopped celery, onion and potatoes. Cover pot and stew vegetables over low heat for 10 minutes without browning. Add stock and herbs; cook vegetables until soft, about 30 minutes. Puree the mixture in a blender. Stir in milk and adjust seasonings. Toss in grated carrot and celery. Reheat to just below the boiling point. Serve with fresh bread.