To make the Green Chile Mayo: Heat the oven to 400 degrees F. Place poblano on a foil-lined baking sheet. Roast for 15 minutes, or until the skin is blistered and blackened. Place the pepper in a zip-top plastic bag, seal and let it stand for 10 minutes. Peel, remove the seeds and finely chop.
Combine the poblano, mayonnaise, garlic and lime juice in a food processor and process until smooth. Season to taste with salt and pepper. Refrigerate for up to 1 week.
The make the Chorizo Burgers: Preheat the grill to medium-high.
Place the chorizo in a food processor, and process until finely chopped.
Transfer the chorizo to a large bowl and add the ground pork, garlic, Worcestershire sauce, Creole seasoning, salt and cayenne pepper.
Using your hands, mix gently but thoroughly. Form the mixture into four 1-inch-thick patties, about 8 ounces each.
Place the patties on the grill and cook to a minimum temperature of 160 degrees F, 5 to 7 minutes per side.
Transfer the burgers to a plate or platter and top each one with a slice of cheese.
Toast the open buns on the grill, if desired.
Place the burgers on the bun bottoms. Generously top each burger with Green Chile Mayo, and place the tops of the buns over the sauce. Serve immediately.