Ingredients:

1 Tbsp olive oil
1 1/2 cups chopped yellow onion (1 medium)
1 1/4 cups chopped celery (about 3 ribs)
1 tsp minced garlic (1 clove)
4 cups unsalted chicken broth
4 cups water
1 (16 oz) bag dried split peas, picked over and rinsed
2 bay leaves
1 1/2 tsp chopped fresh thyme, or 1/2 tsp dried
Salt and freshly ground black pepper
1 1/2 lb meaty ham bone or ham shanks
1 cup chopped carrots
Chopped fresh parsley, for garnish (optional)

Instructions
Heat olive oil in a large pot over medium-high heat. Add onion and celery and saute 3 minutes. Add garlic and saute 1 minute longer.
Pour in chicken broth and water. Add split peas, bay leaves and thyme. Season lightly with salt and with pepper to taste (I like to wait to add more salt until the end to see how salty the ham has made the soup).
Nestle ham bone into soup mixture. Bring mixture to a boil, then reduce to low. Cover and let simmer, stirring occasionally until peas and ham are tender, about 60 - 80 minutes.
Remove ham from soup, let rest 10 minutes then shred or dice meat portion into pieces, cover.
Meanwhile add carrots* to soup. Cover soup and continue to simmer, stirring occasionally, until peas have mostly broken down, about 30 minutes longer**.
Stir ham into soup, season with more salt as needed. Serve warm garnished with parsley if desired.