Prepare the Big Mac Sauce: In a small bowl, mix mayonnaise, diced pickles, mustard, ketchup, and paprika. Stir well and refrigerate until ready to use.
Cook the Beef: In a skillet over medium heat, sauté the diced onion until translucent. Add the ground beef, seasoning with salt, pepper, and garlic powder. Cook until browned, breaking it into crumbles. Drain any excess grease if necessary.
Assemble the Wraps: Lay out the tortillas. Evenly distribute the cooked beef onto each tortilla. Top with shredded lettuce, sliced pickles, and shredded cheddar cheese. Drizzle with Big Mac sauce.
Wrap and Serve: Fold the sides of the tortilla in slightly, then roll it up tightly. Serve immediately or toast the wrap in a skillet for a crispier texture.