Preheat the slow cooker if necessary; see the manufacturer's instructions. Drain the peas and add to a large saucepan with the onions, celery, carrot and water. Bring to the boil, skim if needed and boil for 10 minutes.
Pour the mixture into the slow cooker pot, then stir in the mustard, bay leaf and some black pepper. Rinse the bacon joint in several changes of cold water, then add to the pot and press below the surface of the liquid. Cover and cook on high for 5–6 hours or until the peas are soft and the bacon cooked through.
Lift the bacon joint out of the slow cooker pot with a carving fork, drain well, then cut away the rind and fat. Cut the meat into bite-sized pieces. Purée the soup with a stick blender or leave chunky, if preferred. Stir the bacon back into the pot and mix in the parsley. Taste and adjust the seasoning, adding salt, if needed. Ladle the soup into bowls and serve with crusty bread.