In a medium bowl, combine mayonnaise, lemon juice, grated Parmesan cheese, Dijon mustard, Worcestershire sauce, and minced garlic. Whisk until smooth, then slowly drizzle in olive oil while whisking. Season with salt and pepper.

In a large mixing bowl, toss together shredded lettuce or spinach, sliced avocado, and chopped basil. Drizzle half of the dressing over this mixture, folding until well coated.

Warm the tortillas in the microwave for about 20 seconds until soft. Spread basil pesto evenly over each tortilla.

On each tortilla, layer the salad mixture, followed by grilled chicken, cooked bacon, crumbled cheese, sliced red onion, cucumbers, and cherry tomatoes.

Drizzle remaining dressing over the fillings. Roll each wrap tightly, folding in sides to secure the fillings.

Slice and serve, or heat them in a skillet for a few minutes until golden and crispy.