Chicken: Slice the chicken breast into tenders and season with 1 tsp each salt & pepper. Preheat a large pan to medium-high heat. Add 1 tsp neutral oil. When hot, add the chicken breast pieces and cook for 5-8 minutes, until cooked, stirring frequently. Once chicken is cooked, remove from the heat and set aside.
Prep toppings & coleslaw: Finely dice 1 small onion and set aside. Finely shred 1 carrot and 1/8 purple cabbage, add to a bowl. Add 4 tbs smoky aioli to the cabbage and carrot and mix well. Add more sauce if needed, and set aside.
Make sauce: Combine 2 cups water, 2 tbs tomato paste, 2 tbs adobo sauce, 1 tsp crushed garlic and 1 tsp corn starch in a small saucepan and bring to a simmer. Continue stirring until thick and smooth.
Assemble: Shred the cooked chicken pieces and add to a bowl. Add 1/4 cup of sauce and mix well. Preheat a clean pan to medium-high heat. Dip one wrap in the sauce, coating both sides, and lay on the pan. Add saucy chicken, chopped onion, grated cheese and fresh coriander, then close the wrap. Sear on both sides until golden and crisp. Top with coriander, onion and serve with a few lemon wedges and extra sauce.