Combine onion and salt in colander and let sit for 30 minutes, tossing occasionally. Transfer to clean dish towel, gather edges, and squeeze onion dry.

Spread onion on rimmed baking sheet, sprinkle with pepper, and toss to combine. Divide onion mixture into four 2-inch-wide mounds. Divide beef into 4 lightly packed balls. Place balls on top of onion mounds and flatten balls firmly so onion adheres and patties measure 4 inches in diameter.

Melt butter with oil in 12-inch nonstick skillet over medium heat. Using spatula, place patties onion side down in skillet and cook until onion is deep golden brown and beginning to crisp around edges, 6 to 8 minutes.

Flip patties, increase heat to high, and continue to cook until all browned on second side, about 2 minutes. Place 1 slice American cheese on each bun bottom and top each with burger and bun top. Serve.

WHY THIS RECIPE WORKS During the Depression, enterprising cooks in Okla­homa discovered that they could mash thinly sliced onions into ground beef patties as a way to use less meat without reducing portion size. This trick not only bulked up the patties, but it also created a delicious layer of caramelized onions on the outside that infused the meat with rich­ness. What started out of necessity became a tradition. Our version focuses on flavor,, not thrift. We sliced an onion as thin as possible and salted the slices to draw out moisture so they'd caramelize fully, squeez­ing the salted onion in a dish towel to dry them further. We then formed the patties by making a small mound of onion, placing a loosely formed ball of ground beef on top, and pressing the beef into the onion. We cooked the patties, onion side down, over gentle heat until the onion layer developed a deep golden-brown color and began to crisp. Layering the finished burgers on top of-rather than beneath-the cheese kept the onions crisp.