Heat olive oil in a cast iron dutch oven or soup pot over medium/high heat.
Add onion, celery, and carrots and sauté for three minutes or until the veggies start to become translucent.
Pour in chicken stock, water, split peas, garlic, bay leaves, and thyme.
Add the ham bone into the soup and bring mixture to a boil. Cover and simmer for about an hour, or until the peas are tender.
Remove the ham bone from the soup, and allow it to cool.
Take the meat off the bone and add it back to the soup.
Remove bay leaves.
Add salt and pepper to taste.
Serve into bowls and top with homemade sourdough croutons.
Notes
If you do not have a ham bone or shank, you could substitute it with a couple pieces of uncooked bacon.
For a vegetarian version, use all vegetable broth instead of chicken stock and water, and skip the ham bone. It will have a different and milder flavor, but you'll still find it yummy. You may want to add some more herbs, though, to boost the flavor.