Rinse and sort peas. Heat peas and water to boiling in Dutch oven. Boil uncovered 2 minutes. Simmer on low 1 hour.
Stir onion, celery and pepper. Add ham shanks. Heat to boiling; reduce heat. Cover and simmer about 2 hours or until peas are a little mushy.
Remove ham bone; remove ham from bone. Trim excess fat from ham; cut ham into 1/2 inch pieces. (If you would like to skim the fat, do so now).
Stir ham and carrots into soup. Heat to boiling; reduce heat. Cover and simmer until carrots are tender and soup is of desired consistency, about 30 minutes. Add salt and extra pepper (if needed) to taste.