In a food processor, pulse the chickpeas, green chiles and parsley until finely chopped. Transfer the mixture to a medium bowl and stir in the bread crumbs and salt and pepper to taste. Stir in the egg and form the mixture into 4 patties, each about 2/3 inch thick.
In a large skillet or grill pan, heat the oil over medium-low heat. Cook the burgers for 4 minutes, then flip and cook for 3 minutes more. Top the patties with the cheese slices for the last minute of cooking. Serve the cheeseburgers on the hamburger buns with mustard, ketchup or mayonnaise.