Make the sauce by combining the soy sauce, peanut butter, honey, rice vinegar, sesame oil, garlic, and sriracha in a small bowl. Add two tablespoons of the sauce mixture to the ground chicken and set the sauce aside.
Heat a skillet over medium-high heat and add 1 tablespoon of avocado oil. Using a spatula, break down the chicken in the skillet. Cook for 5-7 minutes, until chicken is completely browned and cooked through. Transfer cooked chicken to a clean bowl and set aside.
To the skillet, add the green onion whites, grated ginger, and minced garlic. Saute for 1 minute adding more oil if needed.
To the skillet, add the red pepper, water chestnuts, cooked ground chicken, and the remaining sauce mixture. Cook for 3-4 more minutes, remove the skillet from the heat and stir in the green onions.
Wash the bibb lettuce, pat dry with a paper towel, and place the leaves onto a plate. Scoop a small portion of the chicken mixture into each lettuce cup. Top each one with sesame seeds and shredded carrots.