Make the sauce by combining all sauce ingredients in a bowl or mason jar. Set aside.
In a large pan, brown the chicken in 1 tbsp oil. Cook whole until a good crust forms before breaking it apart.
Meanwhile, dice the peppers and shred carrots (if not already shredded).
Finish breaking up the ground chicken with a spatula for 2-3 min more.
Once chicken is cooked, add garlic, ginger, cayenne and cook for 1 minute.
In a small dish, mix 1 tbsp arrowroot and 1 tsp water. Add cornstarch mixture to the chicken and combine.
Saute chopped peppers in avocado oil in a different pan or next to the browned chicken. Add bell peppers and shredded carrots to the chicken mixture.
Toss the mixture with sauce and serve warm over lettuce wraps.