Heat peanut and sesame oil in wok over medium high heat.
Fry chicken until outsides are cooked – pink is no longer seen, about 1-2 minutes.
Add onions and carrots and cook until slightly softened, about 2 minutes.
Add red bell Peppers, mushrooms, and garlic and cook for 1 minute.
Add cashew nuts and cook for 1 minute.
Add the soy sauce, shaoxing rice wine, oyster sauce, dry mustard, sugar, chili oil, and cornstarch. Bring sauce to boil (to activate cornstarch) and remove from heat.