In a large mixing bowl, add in the chicken, tomato paste, oil, lime juice and seasonings (garlic powder, onion powder, paprika, cumin, oregano, salt, black pepper and cayenne pepper). Thoroughly mix to combine. Cover the bowl and refrigerate for at least 30 minutes to 1 hour in the fridge.
Prepare the veggies. Heat oil in a large pan over medium heat. Add in the veggies, season with salt and pepper to taste, and cook while stirring until the veggies are mostly tender but still have some crisp, about 6 to 8 minutes, or longer as needed. Transfer cooked veggies to a plate and set aside.
In the same pan used to cook the veggies, heat up some oil (about 2 tablespoons) over medium heat. Add in the marinaded chicken and cook while stirring occasionally until the chicken is thoroughly cooked, about 8–10 minutes or longer as needed. Set aside to cool.
In a large pan over low heat, briefly warm up the tortillas on both sides. Transfer to a plate and keep covered with a clean kitchen towel or aluminum foil.
Working with one tortilla at a time, place down on a clean work surface. Spread 1 to 2 tablespoons of the chipotle sauce into the center of the tortilla.
Next, add over the sauce a layer of cheese, veggies, chicken and some cilantro. Drizzle over some more sauce and top with a few cooked fries (optional but recommended). Firmly fold the outer sides of the tortilla over the filling to form a wrap.
In a lightly oiled pan over medium heat, add the folded wrap and toast on both sides to seal. Repeat with remaining tortillas and fillings for a total of (4) wraps.
Serve wraps immediately as is or with fries and a side of chipotle crema sauce. Enjoy!