Turn your broiler on high and let the oven get hot. Position your rack in the top of the oven, just below the broiler. While the oven heats, if you are making the special sauce, mix together ingredients and set aside for later.
Place onions in an even layer on the bottom of a ¼ sheet pan. Sprinkle with a generous pinch of Momofuku Savory Seasoned Salt and place under the broiler for 3 minutes.
Combine ground beef, 2 tablespoons of Momofuku Soy Sauce, and 3 tablespoons of Momofuku Savory Seasoned Salt. When onions are cooked, remove from the oven and sprinkle with ground beef, pressing it into an even layer across the top of the onions all the way to the edges of the pan. (It should be a very even layer without gaps.) Sprinkle with more Momofuku Savory Seasoned Salt, then broil for 5 minutes.
Remove from the oven, top with American cheese and sliced tomatoes and return to the broiler for 1 minute. Rest for 2–4 minutes.
Prepare your platter. Cut your rolls in half and place the bottom layer on the platter. Spread the top half with the special sauce. Gently edge your burger on top of the bottom layer of rolls. (If you lose some onions, you can just throw them on top.) Top with lettuce and top layer of your rolls. Serve immediately.
