1. Wash the split peas thoroughly under cold running water and continue to wash until the draining water runs clear. Pick over the peas and discard any discolored ones.
2. In a heavy 4- to 5-quart saucepan or soup kettle, bring the chicken stock to a boil and drop in the peas slowly so that the stock does not stop boiling.
3. Add the onions, celery, cloves, bay leaf and mint. Reduce the heat and simmer with the pan partially covered for 1½ hours or until the peas can be easily mashed with a spoon. Remove the bay leaf.
4. Puree the soup through a food mill or fine sieve into a large bowl, and then rub it through the sieve back into the saucepan or into another bowl.
5. Add the salt and pepper, and chill the soup in the refrigerator. (If you wish to serve the soup immediately, place the soup in a bowl and set the bowl in a larger container filled with crushed ice or ice cubes.
6. With a metal spoon, stir the soup until it is ice cold.) Before serving, stir in ½ to 1 cup of chilled heavy cream, thinning the soup as desired, and taste for seasoning. Garnish with sprigs of fresh mint.
