Prep the fatback: If very salty, rinse well under cold water. Pat dry and cut into several large chunks.
Assemble the crockpot: Add split peas, onion, carrot, celery, garlic, fatback, bay leaf, thyme, broth, water, and potatoes (if using). Stir gently to mix.
Cook: Low 8-9 hours or High 4-5 hours, until peas are very soft and starting to break down.
Finish: Remove bay leaf and large pieces of fatback (chop and stir some back in if you like). Use a spoon or immersion blender to reach your desired consistency.
Season & serve: Taste and adjust with a splash of vinegar or lemon juice if needed to balance saltiness. Good served hot with crusty bread or baked potatoes!