Special equipment: 4-inch ring cutter
Place a small piece of plastic wrap inside of a 4-inch ring cutter. Place about 8 ounces of the ground beef onto the plastic and lightly press into the mold just to flatten a touch. Repeat with the remainder of the ground beef.
In a cast-iron pan, heat the oil until it begins to smoke. Sprinkle the burger patties lightly with salt and pepper and place into the hot pan. Sear the burgers, about 4 minutes, on one side. Flip and top each with 2 slices of the cheese. For medium rare, cook another 4 minutes on the other side. Remove the burgers from the pan and rest the meat, 10 minutes.
In the meantime, toast the buns; place them cut-side down in the hot pan until lightly golden brown. In a medium bowl, toss the lettuce leaves with the red wine vinegar, olive oil and some salt and pepper.
To assemble, place a burger atop the bottom half of each bun, top with a lettuce leaf and slice of tomato. Spread each bun top with some Special Sauce, and then serve with a pickle spear.
Combine the ketchup, mayonnaise, cornichons, horseradish and shallots together and season with some salt and pepper.
I like a 50/50 mix of short rib to brisket for my burger meat. If it's not ground to order, I recommend a ground beef mix with at least 30 percent fat. If you press the meat too much while forming the patties, you will make the burgers dense and chewy. The patties will not be perfectly round; they should look rustic.