There are plenty of ways to gussy up a burger. But to make one that's as mouthwatering as it is classic, all you really need is good old American cheese and just the right amount of fat in your ground beef.
Divide the meat into 4 equal portions, about 6 ounces each. Place 1 portion on a work surface. Cup your hands around the meat and begin to gently shape it into a rounded mound. (Use light pressure as you shape so that you don’t pack the meat too tightly.)
Lightly press down on the top of the meat with your palm to gently flatten it. Continue rotating and cupping the meat, patting the top of it occasionally, until you've formed a 4-inch diameter, ¾-inch-thick patty. Using your thumb, make a small indentation in the center to help keep the burger flat as it cooks. Repeat with the remaining portions. Transfer to a plate, cover with plastic wrap, and chill until ready to cook.
Build a medium-hot fire in a charcoal grill, or heat a gas grill on high heat. Brush the grill grate with oil. Season the patties on 1 side with the salt and pepper. Place on the grill, seasoned side down, then season the other side. Grill until lightly charred on the bottom, 3-4 minutes.
Turn and top with the cheese. Grill to the desired level of doneness, 3-4 more minutes for medium-rare burgers. Transfer to the rolls and let stand for 3 minutes before serving.