Wash peas and soak them in water overnight, for at least 8 hours.
If using salted pork, cut in thick slices and boil in water for 10 minutes before dicing. In a large heavy-bottomed pot, fry bacon or pork until it starts to brown.
Add onion and celery and cook until soft.
Add chicken broth, drained peas, carrots, bay leaf, savory, and parsley. Bring to a boil. Let simmer for two to three hours, until peas are tender. Stir soup from time to time to prevent it from sticking.
Season with salt and pepper at the end.
Serve in bowls with parsley and heavy bread on the side.