Bring a medium pot of water to a boil. 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.
Photograph by Christopher Testani
Courtesy of Food Network Magazine