In a mixing cup, combine the hoisin sauce, soy sauce, rice vinegar, and sesame oil. Stir well and set aside.
In a skillet with a lid, over medium heat, add the vegetable oil and ground chicken or turkey. Cook until meat is lightly browned.
Add the minced garlic and grated ginger. Cook for one minute.
Add the chopped mushrooms, stir to combine, and cover skillet and cook for a couple of minutes. The mushrooms will release their water. Stir well to combine.
Add the coleslaw mix, stir, and cover. Cook for two minutes or until the coleslaw mix is slightly soft
Add the white and light green portions of the sliced green onions. Add the chopped water chestnuts and stir.
Add about half of the sauce mixture that was set aside. Stir to combine add more sauce depending on your preference. Any leftover sauce can be added to the lettuce wraps at the table.
To serve, fill each leaf of the butter lettuce with the chicken or turkey mixture. Top with any extra sauce, thinly peeled carrot, and the green parts of the green onions and hot pepper flakes if desired.