Drain the black-eyed peas and transfer them to a 3-quart saucepan. Add the bay leaf, onion slice, basil sprig, and garlic. Add about 8 cups of cold water. Bring to a boil. Simmer uncovered over medium heat, stirring occasionally, for about 1 hour or until the peas are tender.
In a large bowl, whisk together the vinegar, lemon juice, minced fresh basil, chives, and black pepper. Set aside.
While the peas are cooking, blanch the carrots in boiling water for 3 minutes, or until crisp. Drain and add to the bowl with the dressing. Stir well and Set aside.
When the peas are tender, drain and discard the bay leaf, onion, basil, and garlic.
5. Combine peas and carrots and stir lightly to blend. Add the green peppers and red onion. Toss well. Serve chilled or at room temperature.Servings: 6