Combine first 8 ingredients for the sauce and set it aside. In a bowl, combine the next 3 ingredients, Add the chicken and toss.
Heat a frying pan to high heat. Add oil. Heat to hot, not smoking. Add chicken, ginger, garlic and onion. Fry and stir until chicken is opaque, about 1 minute. Add peppers and carrots. Stir 2 - 3 minutes. Add snow peas and the sauce. Cook until it comes to a boil. Add the cashews and serve.