Rinse the ham hock and place it in a large saucepan or Dutch oven along with the broth, split peas, carrots, celery, onion, garlic, bay leaf, thyme, and 1 teaspoon salt. Bring to a boil. Reduce heat and simmer, covered, stirring occasionally, until the vegetables are very tender, 3 to 3½ hours.
Remove and discard the bay leaf. Transfer the ham hock to a plate and let sit until cool enough to handle, at least 10 minutes. Shred the meat and stir it into the soup.