1-Heat a large cast-iron skillet over medium heat. Toast the split hamburger buns, cut-side down, until golden brown on the bottom, about 1 to 2 minutes. Transfer to plates or a serving platter with the cut-side up. Turn off the heat.

2-Divide the 1 pound of ground beef into 4 portions, gently roll each into a ball, and press each into a 3-inch wide patty. Season all over with the 1 teaspoon of kosher salt and 1/4 teaspoon of freshly ground black pepper. Divide the thinly sliced onion (from 1 medium onion, yielding 1 1/2 to 2 cups) between the patties, piling it high.

3-Heat the skillet over high heat until very hot. Place two patties in the skillet with the onion-side up, spaced apart. Use a non-slotted flat metal spatula to press the patties as thin as possible, pressing in different spots to embed the onions. Cook until browned on the bottom and gray around the edges, about 2 to 3 minutes.

4-Carefully flip the patties, scraping up the crust and onions from the bottom. Top each patty with 1 slice of American cheese. Cook until the other side is browned and the cheese is melted, 1 to 2 minutes. Transfer the patties to the bottom bun halves and add any remaining onions on top.

5-Repeat the process with the remaining patties. Add the desired toppings, close the burgers with the top buns, and serve immediately.