Heat the oil in a medium skillet over medium-high heat. Add the chicken, chili powder, paprika, cumin and some salt and pepper to the skillet and cook, stirring occasionally, until the chicken is evenly coated with the spices, browned and cooked through, 5 to 7 minutes. Set aside.
To make the dressing, mix the mayonnaise, Dijon mustard, adobo sauce, garlic salt, Worcestershire sauce and salt and pepper to taste in a medium bowl until well combined. Add the romaine lettuce and toss until well coated. Then add 1/2 cup of the Parmesan and toss again.
Lay out the tortillas and top each one with half of the dressed romaine, tomatoes, Cheddar cheese and taco chicken. Sprinkle each with 2 tablespoons Parmesan. Roll up the tortillas, leaving one end open, then wrap in sandwich paper, leaving 1 to 2 inches of the wrap open and exposed. Enjoy, removing the paper as needed. To transport, cover each wrap entirely in foil.