Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain; rinse under cold water and set aside.
While the pasta is working, in a large bowl, whisk together the peanut butter, honey and 1/4 cup warm water. Whisk in the tamari, lime juice, hot pepper sauce and garlic. Pour in the oil in a steady stream, whisking to combine. Add the reserved noodles and toss to coat.
Place the noodles in 4 shallow bowls and top with the chicken, spinach, carrots, scallions, peanuts and cilantro.