Heat the olive oil in a large pot or Dutch oven over medium-high heat.

Add the diced onion, carrots, and celery to the pot and sauté for 3 to 4 minutes, until the onions become translucent.

Stir in the minced garlic and cook for another minute until fragrant.

Add the rinsed split peas, dried thyme, 1/2 teaspoon kosher salt, and 1/2 teaspoon freshly ground black pepper to the pot, stirring to combine.

Pour in the chicken broth and 3 cups of water, then add the bay leaf and the ham hock to the pot.

Bring the mixture to a boil, then reduce the heat to a gentle simmer, cover, and cook for 50 to 60 minutes, stirring occasionally, until the split peas have broken down and the soup has thickened.

Carefully remove the ham hock from the pot, let it cool slightly, then remove and dice the meat (about 1 cup) and discard the bone and any skin or excess fat.

Return the diced ham to the soup and continue to simmer uncovered for an additional 5 to 15 minutes, or until the soup reaches your desired thickness.

If the soup is too thick, add up to 1 more cup of water; if it's too thin, whisk 2 teaspoons of cornstarch with 1/3 cup cold water to form a slurry, then stir into the soup and simmer for a few minutes until thickened.

Discard the bay leaf, ladle the hot soup into bowls, and garnish with finely chopped fresh parsley, croutons, and an optional sprinkle of flaky kosher salt.