Prepare the chicken: Toss chicken with paprika, parsley, garlic powder, and salt. Grease and heat a grill or sauté pan and cook until cooked through and lightly browned. Slice or chop into bite-sized pieces (alternatively, use prepared grilled chicken).
Prepare the dressing. In a small bowl or container, whisk together mayonnaise, oil, garlic, mustard, Worcestershire (or soy) sauce, and salt until smooth. (The original recipe includes 1 tablespoon water, but we prefer to leave it out for a thicker dressing.)
In a large bowl, combine lettuce, chicken, onion, tomatoes, and dressing. Toss until evenly coated. Alternately: If you prefer your lettuce extra crisp, skip the tossing step. Instead, layer the lettuce, chicken, onions, and tomatoes directly onto each wrap and drizzle with dressing before rolling.
Divide the mixture among the wraps. Fold in the sides and roll tightly pulling it in. Heat a grill pan over medium heat and drizzle lightly with oil. Place the wraps seam-side down on the grill pan and cook until lightly toasted. Turn and grill the second side until golden and crisp.