Heat the oil in a large saucepan over medium-high heat. Add the onion, carrot, and celery and cook until tender, 5 to 7 minutes.
Add the broth, ham, split peas, and thyme to the saucepan; season with ¾ teaspoon salt and ¼ teaspoon pepper. Reduce heat and simmer until the peas are tender, 55 to 65 minutes. Top with croutons.