Season the chicken strips with salt and black pepper and set up separate shallow bowls of flour, beaten eggs and panko.
Coat each strip in flour, egg and panko, pressing the crumbs firmly, then rest the breaded chicken for 8 minutes.
Heat the canola oil in a wide heavy skillet to 350°F and fry 4 strips at a time for 4 to 6 minutes, turning once and maintaining at least 335°F, until crisp and 165°F inside.
Drain the strips on a wire rack and cool them for 5 minutes.
Warm the tortillas briefly and divide the romaine, Parmesan, dressing and chicken strips evenly down their centers.
Fold in the sides, roll each wrap tightly and place seam-side down before cutting in half.