Cover soup mixture tightly and simmer until peas are soft, approximately 45-minutes. Add ham bone and all remaining ingredients. Cover again and simmer until vegetables are all tender, approximately 45-minutes. Lift out ham bone and remove any pieces of meat from the bone to return to the soup, then discard the bone. Taste and adjust seasoning with salt and pepper.
Any additional salt required depends on the saltiness of the ham.
Serve hot, garnished with oyster crackers.