Make the vinaigrette: Place all the ingredients in a large bowl and whisk until well-combined.
Make the cowboy caviar: Add the black-eyed peas, black beans, garlic, tomatoes, bell pepper, jalapeño, red onion, and corn to the bowl of dressing and toss until well-coated. Refrigerate for at least 1 hour, then toss again and garnish with cilantro. Serve with tortilla chips, on a salad, or in a tortilla.