It's easy enough to pick up a chicken Caesar wrap at any local deli or sandwich shop, but making your own at home has a number of definite advantages. First of all, doing it yourself means you can adjust the amount of dressing to your taste preferences — no need to worry about grabbing a soggy wrap. Additionally, since Caesar dressing traditonally includes anchovies, making homemade dressing allows you to add as much or little as you'd like. Another pro that comes with making these wraps at home is that you can add as many toppings as your heart desires (without having to pay a dollar extra for chopped avocado or tomatoes).
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Whisk together the first 6 ingredients (from the olive oil to the pepper flakes) in a mixing bowl, toss the tenders in the marinade to coat, then transfer to an airtight container and refrigerate for at least 2 hours.
About an hour before you're ready to assemble the wraps, heat a grill pan over medium-high heat, then grill the chicken tenders until they are fully cooked, about 6-8 minutes on each side. Remove the chicken from the pan and transfer to the refrigerator to cool.
Whisk together the first 6 ingredients in a large mixing bowl until fully combined; then, in a slow, steady stream add the olive oil while whisking vigorously to form the dressing. Season with salt and pepper, to taste.
Add the lettuce, Parmesan, croutons, tomato, avocado, and chicken to the large mixing bowl with the dressing and toss to fully coat. Add the filling to the wraps or tortillas, roll them up, and serve immediately.