On each of 6 of the patties, arrange and slightly overlap 8 cheese quarters to within 1/2-inch of edge. Top each with the remaining 6 patties. Pinch edges of top and bottom patties together to form one large burger patty, sealing all holes. You will have a lump in top of the patty where the cheese lies inside. Chill patties, covered, in refrigerator for at least 1 hour.
In a large bowl, combine soft bread crumbs and milk. Let stand for 5 minutes. Stir in egg, dry bread crumbs, Worcestershire sauce, salt and pepper. Add ground beef. Combine very lightly with a fork.* Shape meat mixture into twelve 1/2-inch-thick patties, about 3 1/2 inches wide.
For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above the pan. Place burgers on grill rack over the drip pan. Cover and grill for 14 minutes. Turn burgers with a wide spatula. Grill 10 to 12 minutes more or until done (an instant-read thermometer inserted into patties should register 160°F). (For a gas grill, preheat grill. Reduce heat to medium. Adjust heat for indirect cooking. Place patties on grill rack and cover and grill as above.)
During the last 1 to 2 minutes of grilling, open the buns and place them cut-side down on the grill to lightly toast. Remove burgers and buns. Let burgers stand for 2 to 3 minutes before eating (the cheese inside is extremely hot.)
Serve in buns with assorted condiments, such as ketchup, chopped pickled peppers, chopped or sliced tomatoes, and/or pickle relish.
Ingredients need to be evenly distributed, but is important to handle ground meat mixture as little as possible for a more tender, moist burger.
Avoid the temptation to press down on your burger patties to speed up the cooking process. That just releases all the good juiciness, leaving you with a burger that's dry.