In a large bowl, combine the ground chicken, egg, mayonnaise, panko breadcrumbs, and Shake That seasoning. Mix until just combined; do not overwork.
Divide the chicken mixture into 5 equal portions. Spread one portion of the chicken mixture onto each tortilla in a thin, even layer, spreading almost to the edge.
Preheat griddle to medium heat, about 400-425℉. Add about 1 tablespoon of oil to the griddle, and spread it around with your spatula.
While the griddle is heating up, prepare the Caesar salad topping. Add a few spoonfuls of Caesar dressing to the chilled romaine lettuce, and toss to combine. Add in croutons. Refrigerate the salad until ready to use.
Place tortillas meat-side down on the griddle and cook undisturbed for 4-5 minutes, or until the ground chicken is a light golden brown color.
Flip to the tortilla side and continue cooking until the chicken reaches 165°F internal temperature, checked with an instant-read thermometer. Flip back to the chicken side if needed.
Remove from the griddle and top each taco with chilled Caesar salad and a finish of shredded parmesan. Serve immediately.