Handling the chuck as little as possible, divide into forths, shape each forth into a ball, and with your thumb make a depression in the center of each ball. Fill each depression with a piece of cheese and 1 teaspoon of chilies and form the meat around the cheese mixture into a 1-inch patty. Season the hamburgers with salt and black pepper and grill them on oiled grill pan for 5 minutes on each side for medium-rare meat.
Make guacamole with the burgers are grilling: Halve, pit and peel the avocado, in a bowl mash the flesh coarse with a fork, and stir in the lemon juice, tomatoes, scallion, cumin, cilantro and salt & pepper to taste. Transfer the burgers to the buns and then top them with the guacamole.