In a large soup pot, combine dried peas and water or broth and bring to a boil. Cover and simmer over lowest heat for until peas are soft (about 60 minutes). Stir occasionally.

If you prefer a smooth soup, all or part of the soup may be pureed in a scrupulously clean blender or food processor (or this step may be saved for when the jar is opened and served). A hand blender may be used if you want to smooth only a portion of the soup.

Return the pureed soup to the pot and add the remaining ingredients; simmer for another 20 minutes, adding boiling water if needed, if soup becomes too thick. Remove bay leaves.

Ladle soup directly from pot into hot jars, leaving 1-inch headspace. The headspace is important for proper processing. Wipe the rim of the jar clean using a damp paper towel. Adjust two piece lids.

Process pints in a pressure canner for 1 hour and 15 minutes or quarts for 1 hour and 30 minutes (begin counting time when pressure cooker gauge reads 10 lbs PSI or 10 lb setting of weight gauge begins to jiggle).

Allow canner to cool for at least 20 minutes before removing cover (point cover away from you when removing).

Lift jars from canner using a jar lifter and set on a towel to cool for 24 hours before removing jar ring. Inspect seal (cap should be indented downward). Wash jar and store in a cool, dark place.