Start by making the Big Mac sauce. In a small bowl, mix Greek yogurt, Dijon mustard, relish, chopped sweet onion, paprika, onion powder, and garlic powder. Stir until well combined, then let the sauce sit for at least 15 minutes to allow the flavors to develop. While the sauce rests, prepare the toppings by chopping the pickles and shredding the lettuce. Set everything aside for easy assembly.
Divide the ground beef into four equal portions. Roll each portion into a ball, then press it flat between your palms to form thin patties. The patties should be roughly the same size as your tortillas.
Heat a pan over medium heat and let it warm up for about a minute. Add a small drizzle of olive oil to prevent sticking. Place one beef patty in the hot pan and immediately lay a tortilla over it. Use a spatula or your hand to press the tortilla down, smashing the patty underneath. Let it cook for about five minutes, or until the beef is browned and crisp on the bottom. Flip everything so the tortilla is now touching the pan and the beef patty is facing up.
Place a slice of cheese on top of the cooked patty and cover the pan with a lid. Let it sit for one to two minutes until the cheese melts. Keep an eye on it to prevent burning. Once the cheese is fully melted, transfer the taco to a plate and repeat the process with the remaining patties and tortillas.
To assemble, spread a generous spoonful of Big Mac sauce over each taco. Top with chopped pickles and shredded lettuce. Serve immediately while warm for the best texture and flavor.