Rinse lady peas with cold water and remove any hulls and debris.
In a large pot, bring lady peas, broth, garlic, and 2 teaspoons salt to a boil over medium-high heat. Reduce heat to medium-low; cook, covered, until lady peas are just tender but not mushy, about 1 hour, adding more broth if needed. Drain and let cool.
In a large bowl, combine celery, bell pepper, parsley, basil, vinegar, oil, and sugar. Fold in cooled lady peas; cover and chill for at least 1 hour. Add black pepper and remaining ¼ teaspoon salt. Serve over lettuce. Garnish with basil and black pepper, if desired.
Notes
*We used Camellia Brand Lady Cream Peas.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/lady-pea-salad/