Soak and rinse peas for 20 minutes. In a 6-quart pot, combine water, chicken broth, and peas. Bring to a boil. Add ham bone (or ham hocks), carrots, celery, onions, leek, tarragon, and 1 tablespoon parsley, Reduce heat to medium-low and simmer, partially covered, stirring occasionally for 1 hour. Remove from heat.
Remove ham bone or ham hocks and shred meat from bone. Remove any excess fat and return meat to pot. Add sherry, pepper, remaining 2 tablespoons of parsley, and salt to taste. Heat through. (I like to mash up some of the peas and carrots for a thicker soup).