Whisk together mayo, grated onion, ketchup, relish, mustard, vinegar, and paprika to make the sauce. Store in the fridge.
Brown the lean ground beef in a skillet, then drain any excess grease.
Season the beef with salt, pepper, garlic powder, and Worcestershire sauce.
Assemble the wraps by placing lettuce, cheese, onions, pickles, tomatoes, seasoned beef, and Big Mac sauce on the tortillas.
Fold the wraps and secure them with a toothpick. Serve immediately.
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