Saute vegetables: 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.
Add liquid, peas and herbs: Pour in chicken broth and water. Add split peas, bay leaves and thyme. Season lightly with salt and with pepper to taste.
Add ham and simmer: Nestle ham bone into soup mixture. Bring mixture to a boil, reduce to low. Cover and let simmer, stirring occasionally until peas and ham are tender, about 1 hour.
Remove ham, rest then chop: Remove ham from soup, let rest 10 minutes then shred or dice meat portion into pieces, cover.
Add carrots, continue to simmer: Meanwhile add carrots to soup. Cover soup and continue to simmer, stirring occasionally, until peas have mostly broken down, about 30 minutes longer.
Return ham: Stir ham into soup, season with more salt as needed. Serve warm garnished with parsley if desired.
Tips and Variations:
If desired you can add in a couple of yellow or red potatoes when adding the diced carrot to soup to make it even heartier.
If you notice soup isn’t thickening up how you’d like while cooking you can let it simmer uncovered for the last 20 – 30 minutes to reduced down some.
Note that soup will thicken as it rests and cools. The following day, if needed, it can be thinned with more water.