Rinse peas before using. Heat oil in a large soup pot over medium heat. Add onions, carrots and celery and sauté until soft and just beginning to brown, about 10 minutes. Add salt, herbs and spices and sauté for 30 seconds, then add split peas and water. Bring to a boil then reduce heat to a simmer, cover, and cook until peas break down, about 90 minutes. Add cubed ham steak and cook until heated through, about 15 minutes; serve.
Slow Cooker
Rinse split peas before using. Place all ingredients except oil and ham into a slow cooker. Cover and cook until creamy, on low for 3–4 hours or high for 2 hours. Add ham and let heat through before serving.
Multi-Cooker
Rinse split peas before using. Set sauté function to medium heat; add oil. Add onions, carrots and celery and cook until soft, about 10 minutes. Add salt, pepper and herbs and cook until fragrant, about 30 seconds. Add split peas and water. Cover with lid and set the valve to sealing. On manual setting and high pressure, set for 6 minutes. Natural release the pressure for 20 minutes, then add ham. Let ham heat through then serve.