Divide ground beef into 8 equal portions and form into loose balls.
In a small bowl, whisk together mayonnaise, mustard, ketchup, and relish to create the burger sauce.
Preheat a large cast-iron griddle or skillet over medium-high heat until lightly smoking.
Place a beef ball on the griddle and immediately top with a flour tortilla.
Use a heavy spatula or burger press to smash the meat through the tortilla into a thin layer that covers the diameter of the tortilla.
Cook for 2 to 3 minutes until a dark brown crust forms on the beef.
Carefully flip the taco so the tortilla side is down and the beef is facing up.
Immediately place a slice of American cheese on the beef and cook for 1 minute until the cheese melts and the tortilla is toasted.
Remove from heat and top with diced onions, lettuce, pickles, and the prepared sauce before folding.