In a mixing bowl, combine mayonnaise, sugar-free ketchup, mustard, chopped pickles, vinegar, garlic powder, onion powder, and paprika. Whisk until smooth. Cover and refrigerate to allow flavors to meld.

Divide the ground beef into 6 equal portions and gently roll into loose balls. Do not overwork the meat.

Heat a cast-iron skillet or griddle over high heat until very hot. Lightly grease if needed.

Place a beef ball onto the hot surface. Cover with parchment paper and smash firmly with a spatula until very thin. Season with salt and pepper. Repeat with remaining beef.

Cook for 1–2 minutes until crispy and browned. Flip and immediately place a slice of cheese on each patty. Cook another 30–60 seconds until cheese melts.

Remove patties from heat. Add shredded lettuce, pickle slices, and sauce to one side of each patty. Fold gently in half to form a taco-style smash burger.