Heat oil in large, heavy saucepan over medium heat. Add onion, carrot and celery; cook, stirring occasionally, 8 to 10 minutes or until softened. Add ham; cook, stirring, until heated through, 2 to 3 minutes.
Add water, broth, split peas, rosemary, thyme, bay leaf and pepper to onion. Simmer 50 minutes or until peas are tender. Remove bay leaf from soup before serving.