Divide the ground beef into four equal portions. Shape each loosely into a patty about 3/4 inch thick, then press a shallow dimple in the center.
Season both sides with Worcestershire sauce, kosher salt, and black pepper just before cooking.
Heat the neutral oil in a heavy skillet over medium-high heat. Cook the patties for 3 to 4 minutes per side, adjusting for thickness. Use an instant-read thermometer; ground beef should reach 160°F (71°C).
Add cheddar during the final minute of cooking. Cover the skillet briefly to melt the cheese.
Toast the buns cut-side down. Layer lettuce, a patty, tomato, onion, pickles, and mustard or mayonnaise on each bun. Serve warm.