In a small bowl, whisk together the mayonnaise, sweet pickle relish, yellow mustard, smoked paprika, and white vinegar until smooth. Set the special sauce aside in the refrigerator to let the flavors meld.

Divide the ground beef into 8 equal portions and shape them into loose balls. Take one tortilla and press a beef ball firmly onto it, spreading the meat in a thin, even layer all the way to the edges of the tortilla.

Season the beef side of each prepared tortilla evenly with garlic powder, onion powder, salt, and black pepper.

Heat a large skillet or griddle over medium-high heat. Place the tortillas meat-side down onto the hot surface. Use a heavy press or spatula to press down firmly, searing the meat until cooked through and deeply browned.

Flip the taco over so the tortilla side is now facing down. Immediately place a slice of cheese over the hot beef layer. Cover the pan with a lid for about 1 minute until the cheese melts and the tortilla becomes golden and crisp.

Remove the tacos from the skillet. Top each with a handful of shredded iceberg lettuce, diced white onions, pickle slices, and a generous drizzle of the prepared special sauce. Fold slightly and serve immediately.