Rinse split peas; drain. Place drained peas in a 3 1/2-, 4-, or 5-quart crockery cooker. Add the ham bone or pork hocks, onion, celery, carrot, curry powder, dried marjoram or thyme (if using), and bay leaf. Pour chicken broth over all.
Cover; cook on low-heat setting for 10 to 12 hours or on high-heat setting for 4 to 5 hours. Remove ham bone or pork hocks. When cool enough to handle, cut meat off bones; finely chop meat. Discard the bones and bay leaf.
Return meat to crockery cooker. Stir in half-and-half or light cream and, if using, the fresh marjoram or thyme. Season to taste with salt and pepper.