Step 1: Prepare the Big Mac sauce. In a small bowl, whisk together the mayonnaise, sweet pickle relish, yellow mustard, white vinegar, granulated sugar, garlic powder, onion powder, and paprika until smooth and well combined. Cover and refrigerate to allow flavors to meld.
Step 2: Cook the ground beef. Heat a large skillet over medium-high heat. Add the ground beef and cook, breaking it apart with a spoon, until fully browned and no longer pink, about 5-7 minutes. Drain any excess grease. Season the cooked beef with salt and black pepper.
Step 3: Prepare the remaining ingredients. While the beef cooks, shred the iceberg lettuce, finely dice the white onion, and slice the dill pickles. Have your cheese ready.
Step 4: Warm the tortillas. Briefly warm the tortillas in a dry skillet over medium heat for 15-20 seconds per side, or microwave them for 30 seconds to make them more pliable.
Step 5: Assemble the wraps. Lay a warmed tortilla flat. Spread a generous amount of Big Mac sauce over the entire surface, leaving a small border.
Step 6: Add the fillings. Spoon about 1/4 of the seasoned ground beef onto the center of the tortilla, over the sauce. Top with 1-2 halves of American cheese, a portion of shredded lettuce, diced onion, and sliced pickles.
Step 7: Roll the wraps. Fold in the two opposite sides of the tortilla about 1-2 inches towards the center. Then, starting from the bottom edge, tightly roll the tortilla upwards, tucking in the filling as you go, until a secure wrap is formed. Repeat with remaining ingredients. Serve immediately.