Place the split peas in a colander or strainer.
Rinse under cold water and discard any sediment.
Place the peas in a large, heavy saucepan or stockpot with the water and chicken stock.
Cover and bring the liquid to a boil for 2 minutes.
Turn off the heat, leave the lid on, and let the peas soak for at least an hour, or until very tender.
In a heavy skillet, saute the salt pork over medium heat for 5 minutes, stirring occasionally, until it is opaque but not brown.
Add the carrots, celery, and onion and continue cooking until tender, another 6 to 8 minutes.
Add the vegetables and bay leaf, ham hocks, cardamom, salt, and pepper to the pot with the peas, and return to a boil.
Adjust the heat to low and simmer the soup until the meat begins to fall off the bones, 11/2 to 2 hours.
Remove the ham hocks and bay leaf from the soup and pull the meat off the bones.
Discard the bones and bay leaf.
Chop the ham into fine pieces and reserve them until the soup is finished.
Transfer the soup to a food processor fitted with a steel chopping blade.
With an on-off motion, puree the soup until it is slightly chunky.
Return the soup to the pot, add the ham and kielbasa, and simmer for at least 10 minutes to warm the meat.
Taste to adjust the seasonings.