Soak and rinse peas for 20 minutes.
In a 6 qt pot, combine water, broth, and peas; bring to a boil.
Add ham bone, carrots, celery, leek, tarragon, and 1 tablespoon of parsley.
Reduce heat to medium-low; simmer, partially covered, stirring occasionally for 1 hour.
Remove from heat. Remove meat from bone and shred. Remove excess fat and return meat to the pot.
Add sherry, pepper, and remaining 2 tablespoons of parsley. Heat.
Serve hot.