Make the sauce. In a small bowl, whisk mayo, ketchup, mustard, relish, vinegar, onion powder, garlic powder, paprika, sugar (if using), salt, and pepper until smooth.
Taste and adjust. Chill while you cook.
Prep toppings. Shred the lettuce, mince the onion, and slice or chop pickles. Tear cheese slices into halves.
Set everything within reach.
Portion the beef. Divide ground beef into 8–10 equal balls, about 2 ounces each for smaller tortillas or 3 ounces for larger ones. Keep them loose—don’t pack them tight.
Heat the pan. Set a large cast-iron or heavy skillet over medium-high heat. Add a thin slick of oil.
Let it heat until shimmering.
Smash the first taco. Place one beef ball in the hot pan. Immediately press a tortilla on top and use a wide metal spatula (or burger press) to smash the beef flat into the tortilla, spreading almost to the edges. Season the beef side with salt and pepper.
Cook until well browned. Let it sear, beef-side down, for 2–3 minutes until deeply browned and crispy at the edges.
Don’t move it—browning equals flavor.
Flip and melt. Flip so the tortilla is now on the pan and the beef is facing up. Lay a half slice of American cheese on the beef. Cook 30–60 seconds to warm the tortilla and melt the cheese.
Top and sauce. Transfer to a plate.
Add a spoonful of special sauce, then lettuce, onion, and pickles. Fold gently if you like, or serve open-face.
Repeat. Wipe the pan if it gets greasy or smoky and add a touch more oil as needed. Keep building tacos and keeping them warm in a low oven if serving all at once.
Serve immediately. The best texture is hot and fresh, when the beef edges are still crisp and the cheese is gooey.