In large bowl, mix ground pork, onion, garlic and chili powders. Add black-eyed peas and salt; mix well. Form into four loosely packed balls and refrigerate at least 30 minutes.
To make Caramelized Onions: In large skillet over medium-high heat, warm butter. Add onions, water and salt; cook, stirring, until onions soften and turn golden brown, about 5 minutes. Remove from heat and set aside.
To make Charred Green Chili Mayo: Place green chilies in hot cast iron skillet over medium-high heat. Cook, turning, until chilies begin to soften and turn black. Remove from heat and place in small bowl. Add mayonnaise, garlic and lime juice; whisk to blend. Add green onions and cilantro; stir well and refrigerate.
To make burgers: Warm cast iron or nonstick griddle pan over medium-high heat. Place pork balls on hot skillet; flatten with heavy metal spatula. Season with salt, to taste. Cook approximately 3 minutes; flip and cook 2-3 minutes until internal temperature reaches 145 F.
Lightly toast buns. Place each burger on toasted bun with slice of cheese, Caramelized Onions, Charred Green Chili Mayo, avocado and lettuce.