The Basically Burger

Name: The Basically Burger
Ingredients: 20 ounces ground beef, 80% lean; Kosher salt; 2 tablespoons vegetable oil, divided; 2 tablespoons plus ½ cup mayonnaise (preferably Hellmann’s); 4 potato or soft-seeded hamburger buns; 4 slices American cheese; 3 tablespoons ketchup; ¼ cup sweet pickle relish; 1 tablespoon hot sauce (such as Tapatío, Cholula, or Crystal); Freshly ground black pepper; 4 large iceberg lettuce leaves, torn into large pieces; ¼ medium red onion, sliced as thinly as possible