Add the barley, then reduce the heat to medium and simmer 7 minutes; add the black-eyed peas and continue cooking until both the barley and black-eyed peas are tender, about 5 more minutes.
Drain and rinse under cold water.
Whisk the olive oil, vinegar, mayonnaise, 3/4 teaspoon salt, and pepper to taste in a large bowl.
Add the greens, ham, tomatoes, radishes, scallions, pickles, barley and black-eyed peas and toss.
Divide among plates.
Per serving: Calories 376; Fat 15 g (Saturated 2 g); Cholesterol 15 mg; Sodium 472 mg; Carbohydrate 48 g; Fiber 9 g; Protein 16 g