Whisk the sauce: In a bowl, whisk peanut butter, coconut milk, soy sauce, brown sugar or honey, rice vinegar, garlic, ginger, tomato paste, and chili-garlic sauce until smooth.
Add a splash of broth if it’s too thick to pour.
Layer the slow cooker: Place chicken in the crockpot. Add optional veggies on top or around the chicken. Pour the sauce over everything and gently toss to coat.
Cook low and slow: Cover and cook on Low for 4–5 hours or on High for 2.5–3 hours, until the chicken is tender and easily shreds or slices.
Shred or slice: Remove the chicken to a cutting board and shred with two forks or slice into chunks.
Return to the sauce and stir to coat.
Adjust consistency: If the sauce is too thin, whisk cornstarch with a tablespoon of water, add to the crockpot, and cook on High for 10–15 minutes. If too thick, loosen with a bit of warm broth.
Brighten it up: Stir in lime juice. Taste and adjust salt, sweetness, and heat.
Serve: Spoon over rice or noodles.
Top with cilantro and chopped peanuts for crunch.