Place the neck bones in a large pot. Fill with water until the bones are covered. Bring the water to a boil over high heat. Reduce heat and simmer for about an hour, until the meat is tender and easily taken from the bone.
Drain the water from the pot and separate the meat from the bones. Discard the bones and set the meat aside.
Place the pot back on the burner, set to medium heat. Add the oil. Sauté the onion until soft. Add salt and cayenne pepper. Add about 6 cups of water and bring to a boil. Add greens and reserved meat. Cook for about 40 minutes, until the greens are tender.
Refrigerate overnight. Reheat over medium heat before serving.