In a slow cooker, combine split peas, onion, carrots, celery, thyme, ham, 7 cups water, 1 tsp. salt and 1/2 tsp. pepper. Cover and cook on low until peas are tender, 5 to 5 1/2 hours.
Working in batches, finely chop kale in a food processor (you should have about 5 cups). Uncover soup; remove and discard thyme sprigs. Stir in vinegar, then kale. Taste and season with more vinegar, salt and pepper, if desired.