1. In a medium saucepan over high heat, cover black-eyed peas with water. Bring to a boil for 2 minutes, cover, remove from heat and let stand for 1 hour.
2. Drain the water, leaving the peas in the saucepan. Add broth, tomatoes, onion, celery, garlic, mustard, ginger, cayenne pepper, and bay leaf. Stir together and bring to a boil. Cover, reduce heat and simmer slowly for 2 hours, stirring occasionally. Add water as necessary to keep the peas covered with liquid.
3. Remove the bay leaf and serve hot, garnished with parsley.