Arrange the split peas in the slow cooker in an even layer. Arrange the carrots, celery, onion, garlic, parsley, and bay leaf over the peas in one even layer. Place the ham bone or hocks on top of the vegetables. (At this point you can remove the insert from the slow cooker, cover, and refrigerate up to 12 hours until ready to continue.)

Pour the chicken broth and water into the slow cooker and season with salt and pepper. Cover and cook until the peas are very soft and the meat is falling off the bone, on high for 5 to 6 hours or low for 8 to 10 hours.

Remove the ham bone or hocks to a cutting board. When cool enough to handle, remove the meat from the bones, place the meat back in the soup (discard the skin and bones), and stir to combine. Taste and season with more salt and pepper as needed.