Whisk together the mayonnaise, relish, mustard, sugar, vinegar, smoked paprika, onion powder, and garlic powder in a small bowl until smooth and well combined. This sauce is best made first so the flavors can meld while you cook the tacos. I like to let it sit for a minute or two—the paprika really blooms and adds depth to the creamy base.
Finely dice the small onion into 1/4-inch pieces and measure out the dill pickle chips and shredded lettuce into separate small bowls. Divide the ground beef into 4 equal portions (about 4 ounces each), keeping them loose and not packed. Have your tortillas, cheese slices, and salt and pepper readily accessible near your cooking station.
Heat the oil in a large skillet over medium-high heat until it shimmers. Place the first tortilla flat in the pan, then spread one portion of ground beef evenly across the entire tortilla surface. Immediately season generously with salt and pepper, then use a spatula to press the meat firmly into the tortilla for 2-3 minutes, creating a crispy, browned crust. Flip the tortilla, place one slice of cheese on top, and cook for 1-2 minutes until melted. Transfer to a plate and repeat this process with the second taco. I find that pressing down firmly and not moving the meat allows it to develop that delicious crust that makes smash burgers so addictive.
Repeat the same process with the remaining two portions of ground beef and tortillas, cooking them in the same skillet (no need to add more oil). Season with salt and pepper, smash for 2-3 minutes until browned, flip, add cheese, and cook for 1-2 minutes until melted.
Spread a generous layer of the special sauce from Step 1 on top of each taco's melted cheese. Layer the shredded lettuce, diced onions, and dill pickle chips evenly across each taco. Serve immediately while the tortilla and cheese are still warm.