Prepare breadcrumbs. Heat 2 tablespoons olive oil and 1 tablespoon butter in medium sauce pan over medium heat. Add breadcrumbs and stir to combine. Continue to toast until golden brown. Season with Italian seasoning, garlic powder, salt, and pepper and toast for another 30 seconds. Remove from heat and let cool.
Make dressing. Combine all of the ingredients including cheddar cheese, mayonnaise, lemon, garlic, anchovies, Dijon mustard, worcestershire, salt, and pepper in a blender. Puree until smooth and set aside.
Assemble wraps. In a large bowl, combine chicken, romaine, bacon, cheese, and ¾ cup of the breadcrumbs. Add as much dressing as you like and toss to combine.
Lay tortillas on a clean work surface and divide the chicken caesar filling among both tortillas. Wrap tortillas, folding in the edges. Serve immediately.
Notes
Both the breadcrumbs and dressing can be prepared up to 5 days in advance.