Fill a large pot with hot water. Add the rice noodles and cover the pot, allowing them to soak and soften for 8 to 10 minutes, or until they're barely al dente. (Alternately, cook the noodles according to the package instructions.) The noodles will be stir-fried so do not overcook them at this point.
Drain the noodles and rinse them with cold water to prevent them from sticking together.
Cut the chicken breasts into thin, 1-inch slices. Place the chicken in a medium bowl. Whisk together the cornstarch with the soy sauce then pour it over the chicken, stirring to coat.
Heat a wok or large nonstick sauté pan over medium-high heat. Add 1 to 2 tablespoons of vegetable oil then add the minced garlic and crushed red pepper flakes and cook, stirring continuously, for 30 seconds until the garlic is golden brown and fragrant. Add the chicken to the pan (including all liquids), and cook, stirring frequently until it is no longer pink. Add 1 to 2 tablespoons of chicken stock at a time to the pan while the chicken is cooking to prevent it from drying out. (You may not use the entire 1/4 cup of chicken stock.)
Add the noodles to the pan then pour in the prepared sauce. Bring the sauce to a boil, and using two flat spatulas, lift and turn the noodles to combine all of the ingredients. (Don't stir the noodles too vigorously or they'll break.) Continue cooking the noodles for 1 to 2 minutes until the sauce thickens slightly, then add the bean sprouts and cook for 1 more minute. The noodles are fully cooked when they are chewy and no longer crunchy.
Transfer the noodles to serving dishes and garnish with the sliced carrots, shredded red cabbage, cilantro, scallions, peanuts and lime wedges.