Step 1

Special equipment: a 10-by-15-inch rimmed baking sheet

Step 2

Preheat the oven to 425 degrees F. Cut the onion in half, and shred each half on the large holes of a box grater. Squeeze the shredded onion dry between 2 towels, and scatter around a 10-by-15-inch rimmed baking sheet.

Step 3

Put the ground beef, egg, breadcrumbs and 1 teaspoon salt in a large bowl, and mix gently, just enough to incorporate evenly. Drop mounds of the mixture all around the baking sheet, and press them into an even layer without disturbing the onions too much (but expect some of the onions to move around and peek through the meat). Brush the top of the meat with the vegetable oil, then season it evenly with 1/2 teaspoon salt and several grinds of fresh pepper. Score the meat into 24 squares, cutting completely through with a spatula.

Step 4

Bake until browned and no longer pink in the middle, 8 to 9 minutes. Put a small square of cheese on each patty, and return to the oven to melt, about 30 seconds. Let rest a few minutes, then recut along the scores to separate.

Step 5

Top each patty with a slice of tomato and pickle. Slide a spatula into the pan, and let guests serve themselves. Serve alongside a platter with the buns and lettuce. Don't forget the ketchup and mustard.