To a blender or food processor, add the soy, water, sesame oil, honey, sugar, fish sauce, vinegar, garlic, ginger, hoisin, and peanut butter. Process until completely smooth.
Place the chicken pieces in a plastic zipper bag or shallow sealable container. Pour half of the sauce over the chicken, reserving the rest of the sauce. Seal the chicken and refrigerate for at least 2 hours. Refrigerate the other half of the sauce also, separately.
Prepare the rice noodles according to the package directions.
Meanwhile, in a non-stick skillet over medium-high heat, stir-fry the marinated chicken until cooked through and browned, adding the bell pepper and carrots in the last couple minutes of cooking. Stir in the reserved sauce and heat through. Add the noodles to the pan and toss to coat. Remove from heat. Top with peanuts, green onions, and cilantro. Serve promptly with lime wedges and Sriracha.