In a small bowl, whisk together 1 cup mayonnaise, 1/4 cup ketchup, 2 tablespoons yellow mustard, 2 tablespoons sweet pickle relish, 1 teaspoon white vinegar, 1/2 teaspoon smoked paprika and 1/4 teaspoon kosher salt until the sauce turns a smooth, pale orange. Cover and refrigerate it while you prep the beef.

In a large mixing bowl, combine 2 pounds of 80/20 ground beef with 2 teaspoons kosher salt, 1 teaspoon black pepper, 1 teaspoon garlic powder and 1 teaspoon onion powder. Mix with your hands just until the seasoning disappears into the meat, then divide it into 12 even portions, about 2.5 ounces each, and roll each into a loose ball.

Set the beef balls on a plate and refrigerate for 10 minutes. Cold beef holds its shape under the press instead of squishing out sideways.

Heat a large cast iron skillet or griddle over medium-high heat for 3 to 4 minutes, until a flicked drop of water skitters across the surface and disappears in under a second. Brush the surface with 1 tablespoon of the neutral oil.

Set one beef ball in the hot skillet and lay a flour tortilla directly on top of it. Press down firmly with a heavy flat-bottomed pan or a sturdy metal spatula for about 10 seconds, until the beef spreads out in a thin, lacy layer that reaches the edges of the tortilla. Cook undisturbed for 2 to 3 minutes: lift one corner to check for a deep brown, crisp crust before moving on.

Flip the taco so the tortilla side faces down, then immediately lay a slice of American cheese over the hot beef. Cook for 1 to 2 minutes more, until the cheese has fully melted and the tortilla has picked up its own golden, blistered spots.

Slide the finished taco onto a wooden board and tent loosely with foil to keep it warm. Wipe the skillet, add the remaining 1 tablespoon of oil, and repeat the smashing, cooking and cheese steps with the remaining beef balls and tortillas, two at a time if the skillet is large enough, until all 12 are done.

While each taco is still warm and open-faced, top the cheese with a small handful of the 2 cups shredded iceberg lettuce and a spoonful of the 1 cup chopped dill pickles.

Spoon the chilled special sauce over the lettuce, fold each taco in half, and arrange them folded side down on a platter. Serve immediately, while the edges are still crisp.