Place ground chuck in a large bowl and break up with fingers to increase surface area for seasoning. Sprinkle salt and pepper over meat and toss lightly with hands to distribute seasoning. Divide meat into 4 equal portions (5 oz each). With cupped hands, toss portion of meat back and forth to form a loose ball. Pat lightly to flatten to a 1-inch-thick burger, 3-1/2 to 4 inches across, using your fingertips to create a pocked, textured surface. Repeat with remaining meat.
If grilling burgers, heat enough coals to make a hot fire (at least 5 pounds). When coals are hot and covered with white ash, spread them over half of grill. Replace grill rack and lid; heat until grill rack is very hot, about 5 minutes. Place burgers on grill rack over hot coals, cover and grill on one side (see below for exact cooking time). Turn burgers and grill to desired doneness.
If pan-broiling, heat a 12-inch cast-iron skillet over medium-high heat until very hot, at least 5 minutes. When pan is hot (drops of water flicked into the pan evaporate immediately), add patties and cook one side. Turn burgers and cook to desired doneness.
Serve immediately with buns and any desired toppings.