Place black-eyed peas in a large container and cover with at least 2 inches of cool water; let soak, 8 hours to overnight.
Transfer black-eyed peas and water to a pot; bring to a boil. Reduce heat to low and simmer until tender, 15 to 20 minutes. Drain and let cool, about 15 minutes.
Combine black-eyed peas, cabbage, olive oil, green onions, lemon juice, parsley, salt, and pepper in a large bowl. Chill for at least 1 hour before serving.
