Make the secret sauce by combining all the ingredients in a small bowl and whisking until homogenous, then cover and chill until needed.

Prepare the sautéed onion by heating the butter and oil in a medium sauté pan over medium heat. Add the onion and cook for 5 to 7 minutes, stirring occasionally, until the onion is lightly browned. Remove from the heat.

Preheat a large griddle or sauté pan over medium-high heat. Form ½ pound of ground chuck into a thick round patty slightly smaller than the diameter of the buns and place it onto the hot griddle or pan. Season with salt and pepper and after about 1 minute of cooking use a strong spatula to press down on the beef until it spreads out to slightly wider than the diameter of the buns. Cook the beef for 2 to 3 more minutes, or until a dark brown crust forms on the bottom of the patty, then flip it over and cook for 2 to 3 more minutes. Use the spatula to press down on the burger after you flip it so that crust will also form on the other side. Add a slice of American cheese on top of the burger patty approximately 1 minute before you take the burger off the griddle.

While the meat is cooking, brown the face of the hamburger buns in a separate large sauté pan over medium-high heat until golden brown.

When the beef patty is done, build your burger by first spreading some of the secret sauce over the face of the bottom bun. Add about ½ cup of iceberg lettuce, then top the lettuce with one-quarter of the grilled onion. Use a spatula to position the beef patty on top of the onion and lettuce, then slather some more secret sauce on the face of the top bun and crown your burger. Repeat for the remaining 3 burgers.