Pick out any green peas or little pebbles from the dried peas, then rinse them in a colander. There's no need to soak them.
Place the peas, 12 cups of chicken stock, the quartered onion, bay leaves, marjoram, salt, and black pepper in a very large pot. Nestle in the meaty ham bone, then cover and bring to a boil (roughly 15 minutes) then reduce the heat to medium low and simmer for an hour, stirring occasionally.
While it's simmering, use a food processor to chop up the carrots, celery, and onion.
After an hour of simmering, remove the bone from the split pea soup and place on a plate. Discard the quartered onion.
Add the last 3 cups of unsalted chicken broth, onions, carrots, celery, chopped ham, 1 teaspoon of salt and ½ teaspoon black pepper. Stir. Cover with the lid askew and simmer for 30 minutes on medium low, stirring occasionally. After 15 minutes, taste. Adjust seasonings if desired. (If you like it thinner, add more unsalted chicken broth or filtered water.)
When the bone has cooled, cut off the meat and finely chop it. Add most of the ham to the pot, but reserve some for garnish. Taste and adjust the salt or black pepper as desired. Discard bay leaves before serving.
Garnish with finely chopped ham, parsley or green onion. Serve hot with fresh crusty bread.