Make red curry peanut sauce by whisking together smooth peanut butter with coconut milk, brown sugar, soy sauce, red curry paste, fish sauce, and juice of 1 lime until smooth. Set aside.
Mix together hoisin, sriracha, rice vinegar, and sesame oil.
Heat 1 tablespoon oil in a large saute pan over medium-high heat. Add chopped chicken and saute until browned. Add garlic, Thai chile if using, ginger, water chestnuts, carrots, and scallions. Stir to combine and saute for 2 minutes or until the carrots have softened.
Add hoisin sauce mixture and stir to combine. Saute another 1-2 minutes or until everything is well coated in the sauce. Season with salt and pepper and sprinkle chopped peanuts on top.
Serve lettuce wraps with red curry peanut sauce.