Prep the slow cooker base: Add the diced onion, garlic, and ginger to the bottom of your slow cooker.
Whisk the sauce: In a bowl, stir together soy sauce, hoisin, rice vinegar, honey (or brown sugar), sesame oil, chili-garlic sauce (if using), and chicken broth until smooth.
Add the chicken: Place the chicken in the slow cooker, then pour the sauce mixture over it, coating all sides.
Cook low and slow: Cover and cook on Low for 4–5 hours or on High for 2–3 hours, until the chicken is very tender and shreds easily.
Shred the chicken: Transfer the chicken to a cutting board and shred with two forks. Return it to the slow cooker and stir to soak up the sauce.
Thicken the sauce (optional): If you want a stickier finish, stir together cornstarch and water, add to the slow cooker, and cook on High for 10–15 minutes until slightly thickened.
Taste and adjust: Add a squeeze of lime or a splash of vinegar if you want more brightness, or a little honey if you prefer sweeter.
Prep the lettuce and toppings: Separate and rinse lettuce leaves.
Pat dry. Arrange carrots, bell pepper, green onions, herbs, and nuts in small bowls.
Assemble: Spoon warm chicken into lettuce leaves. Top with carrots, peppers, green onions, herbs, and nuts.
Finish with a squeeze of lime.
Serve: Eat immediately while the lettuce is crisp and the chicken is hot and saucy.