Drain the peas, place in medium saucepan with kombu, and add water to cover by 2 inches. Bring to a boil, skim off foam, reduce heat, partially cover, and simmer for 40-50 minutes, until just tender. Add 1 t salt and simmer for 5 minutes, then drain and set aside.
Meanwhile, heat oil over medium heat, add onion and celery, and sauté 5-7 minutes until soft. Add remaining ½ t salt, garlic, and spice blend and sauté 2-3 more minutes, until fragrant.
Cut the tomatoes in half lengthwise, then add to pot along with their juice, veggie stock, and the black-eyed peas. Bring to a simmer, reduce heat to medium-low, cover, and simmer for about 30 minutes, stirring occasionally, until thickened.
Add the basil and cook another minute, then serve hot.