Slice breasts horizontally into very thin slices and cut into inch squares. Set aside.
Prepare vegetables, removing ends and strings from pea pods, slicing mushrooms, green part of onions, and the bamboo shoots. Set aside.
Mix soy sauce, cornstarch, sugar, and salt together.
Heat 1 Tbsp (15 ml) of oil in skillet over moderate-high heat, add all the nuts, and cook 1 minute, shaking the pan, toasting the nuts lightly. Remove and reserve.
Pour remaining oil in pan, fry chicken quickly, turning often until it looks opaque.
Add pea pods, mushrooms, and broth. Cover and cook on low heat for 2 minutes.
Remove cover, add soy sauce mixture, bamboo shoots, and cook until thickened, stirring constantly.
Simmer uncovered a bit more. Add green onions and nuts and serve immediately.