Rinse the dried split peas thoroughly in a colander under cool running water, discarding any debris or stones you might find. Drain well and set aside. This step helps remove excess starch and ensures a clearer soup.
In a 6-quart slow cooker, add the rinsed and drained split peas from Step 1, chicken broth, water, ham bone or cooked ham, diced celery, diced carrots, chopped onion, minced garlic, bay leaf, ground black pepper, and dried thyme. Stir to evenly distribute the ingredients for an even cook.
Cover the slow cooker and cook on high heat for 4-5 hours or on low heat for 8 hours, until the peas are tender and the vegetables have softened. If using a ham bone, you can remove it, shred any remaining meat, and return it to the pot at the end. I personally like to cook this on low for a deeper, richer flavor.
When the soup is fully cooked, remove and discard the bay leaf. Stir in the chopped fresh parsley, and season with additional salt and black pepper to taste. Serve the soup hot, garnished with more parsley if desired.