1 1/2 pounds (80 percent lean) ground beef
1 cup shredded cheddar, Swiss, or Jack or crumbled blue cheese
1 teaspoon salt
1/2 teaspoon pepper
Turn all the burners to high, close the lid, and heat the grill until very hot, about 15 minutes. Clean and oil the grill. Leave all the burners on high.
Meanwhile, spread the meat out over a large plate, sprinkle with the cheese, salt, and pepper, and gently toss the meat with your hands to incorporate the seasonings. Divide the meat into 4 portions and, with cupped hands, toss each portion of meat back and forth from hand to hand to shape it into a loose ball. Using your hands, flatten the balls into 1-inch-thick patties. Press the center of each patty down with your fingertips to form an indentation about 1/4 inch deep. Rub each burger with 1-teaspoon oil.
Grill the burgers indentation-side up, covered, until well seared on the first side, about 3 minutes. Flip the burgers and continue to grill to the desired doneness, 2 to 5 minutes.
Transfer the burgers to a platter, tent with foil, and let rest for 5 minutes before serving.
Charcoal Grilling Method: Build a medium-hot single-level fire and grill the burgers as described in step 3, leaving the grill uncovered.