Black-eyed peas are a staple of New Orleans cooking and this salad is a delicious way to make them part of your meal.
For the black-eyed peas: Heat oil in a large pot over medium heat. Stick cloves into onion pieces; add to pot. Add carrots, celery, ham, and garlic. Cook until onions start to brown, 10 minutes. Stir in wine and peas; cook 1 to 2 minutes. Add water to cover by 2 inches. Cover pot; bring to a boil over high heat. Immediately reduce heat; simmer 30 minutes. Add salt and pepper. Cook until peas are tender, 5 to 10 minutes more. Let peas cool in the liquid, 3 to 4 hours.
For the vinaigrette: Combine lemon juice, cayenne, honey, salt, pepper, and 1 tablespoon of liquid the peas are cooling in. Gradually whisk in oil.
To assemble the salad: Cook lima beans in boiling water until just tender; drain and rinse in cool water. Place in a large bowl. Drain peas; discard cooked vegetables. Add peas to limas. Add celery, onion, carrots, vinaigrette, and oregano; toss gently. Serve at room temperature.