In a large mixing bowl, combine the black beans, black-eyed peas, corn, diced tomatoes, bell pepper, onion, jalapeño, and most of the chopped cilantro, stirring gently to mix everything evenly.
In a separate bowl, whisk together the olive oil, red wine vinegar, lime juice, salt, sugar, grated garlic, cumin, cayenne pepper, and black pepper until the dressing is well combined.
Pour the dressing over the bean and vegetable mixture, then stir thoroughly so all ingredients are evenly coated.
Cover the bowl and refrigerate the mixture to allow the flavors to develop and blend together.
Just before serving, gently fold in the diced avocado, being careful not to mash it.
Taste the mixture and adjust seasoning if needed to balance the flavors.
Garnish with the remaining cilantro and serve with tortilla chips.