Whisk together the mayonnaise, sweet pickle relish, yellow mustard, white vinegar, paprika, onion powder, garlic powder, and white pepper in a medium bowl until completely smooth. Cover and refrigerate for 20-30 minutes while you prepare the other ingredients to allow flavors to meld.

Divide the ground beef into 4 equal portions (about 4 ounces each). Gently shape each portion into a ball without compressing the meat - you want them loosely formed, not tightly packed.

Heat a cast iron skillet or griddle over medium-high heat until very hot (a drop of water should sizzle and evaporate immediately). This usually takes about 3-4 minutes.

Place one beef ball on the hot skillet. Immediately place a small piece of parchment paper on top, then press down hard with a sturdy spatula to smash it thin (about 1/4 inch thick). Remove and discard the parchment paper. Season generously with salt and pepper.

Cook the patty undisturbed for 2 minutes until edges are crispy and deeply brown. Flip once, immediately top with a cheese slice, and cook for another 1-2 minutes until cheese melts and internal temperature reaches 160°F. Transfer to a plate and repeat with remaining patties.

While the last patties are finishing, heat a dry skillet over medium heat. Place one flour tortilla in the skillet and cook for 1-2 minutes per side until lightly charred and puffed in spots. Keep warm and repeat with remaining tortillas.

Spread a generous layer of Big Mac sauce on each warm tortilla. Add shredded lettuce, diced onion, and pickle chips. Top with a cheesy smash burger patty, fold like a taco, and serve immediately. Sprinkle with toasted sesame seeds if desired.