Heat the olive oil in a large pot over medium heat. Add the chopped onion, diced celery, and minced garlic. Sauté for about 5 minutes until the onions become soft.

Stir in the rinsed split peas, then add the broth, bay leaves, and dried thyme. Season lightly with salt and pepper. Nestle the ham bone into the mixture.

Bring the soup to a boil, then reduce the heat to low. Cover and let it simmer for about 60-90 minutes, stirring occasionally.

When the split peas have softened, remove the ham bone and let it cool briefly. Shred any meat from the bone and return it to the pot.

Add the chopped carrots and simmer for an additional 15 to 30 minutes until the carrots are tender. Add additional broth if needed to reach your desired consistency.

Remove the bay leaves, adjust the salt and pepper as needed, and serve warm, with croutons or crusty bread if desired. Garnish with fresh parsley.