Whisk chicken stock, peanut butter, coconut aminos, brown sugar, lime juice, rice wine, chile sauce, garlic, and ginger together in a bowl. Set sauce aside.
Fill a large pot with lightly salted water and bring to a rolling boil; stir in rice noodles and return to a boil. Cook noodles uncovered, stirring occasionally, until tender yet firm to the bite, 4 to 5 minutes.
Heat oil in a skillet over medium heat. Add carrots and cook for 1 minute. Add chicken; cook and stir until chicken is no longer pink inside and juices run clear, 5 to 7 minutes. Add cooked noodles and pour sauce over noodles. Reduce heat to medium-low to prevent overcooking noodles.
Cook and stir until sauce thickens, 3 to 5 minutes more. Stir in bean sprouts and green onions and remove from heat. Garnish with chopped peanuts, cilantro, and sriracha sauce.
