Make the Sauce: In a small bowl, whisk together mayo, ketchup, relish, mustard, vinegar, sugar, paprika, garlic powder, and onion powder until smooth. Set aside to let flavors blend.
Portion the Beef: Divide ground beef into 12 equal portions, about the size of a golf ball. Roll each portion into a ball.
Assemble Before Cooking: Place one beef ball in the center of a flour tortilla. Press down with your hand or the bottom of a plate until beef spreads to cover most of the tortilla in a thin layer. Season the meat side generously with salt and pepper.
Cook the Taco: Heat a large skillet over medium-high heat. Add 1/2 teaspoon oil. Place assembled tortilla meat-side down into the pan. Press firmly with a metal spatula to smash the beef against the hot surface. Cook undisturbed for 3-4 minutes until edges are deeply browned and crispy.
Add Cheese: Flip the taco over so tortilla is on bottom. Immediately place a cheese slice on the hot beef. Let cook for 1 minute until cheese melts and tortilla crisps slightly on the bottom.
Top and Serve: Remove from heat and transfer to a plate. Top with diced onion, shredded lettuce, pickle slices, and a generous drizzle of special sauce. Serve immediately while hot and crispy.