Stir together the mayonnaise, ketchup, relish, vinegar, paprika, and sugar in a small bowl. Set the sauce aside.

Divide the beef into 8 equal portions and shape into thin patties. Season both sides with the onion powder, garlic powder, salt, and pepper. Cook in a large skillet over medium‑high heat for about 2 minutes per side until cooked through. Drain on paper towels.

If not using tostada shells, toast each small corn tortilla in a dry skillet over medium heat for 1 to 2 minutes per side until golden and crisp.

For each wrap, place a large flour tortilla on the counter. Spread sauce in the center, add a beef patty, a slice of cheese, a tostada shell, then lettuce, pickles, onion, and a second patty. Top with more sauce, fold the tortilla edges up and over the fillings, and pleat tightly to seal.

Heat a thin layer of oil in the same skillet over medium heat. Place the wrap seam‑side down, cook 3 to 4 minutes until golden, flip, and cook another 3 to 4 minutes. Slice in half and serve immediately.