Rinse and sort the peas, then place in a medium saucepan with the salt and water. Bring to a boil, reduce heat to low, cover, and simmer for 1 1/2 hours until the peas are tender. Drain any remaining liquid.
Heat the oil in a large skillet over medium heat. Add the onion, celery, bell pepper, garlic, thyme, oregano, and cumin. Cook for 6 to 8 minutes until vegetables are softened.
Add cooked black-eyed peas to skillet and cook an additional 5 minutes. Serve hot over cooked rice.