Cut broccoli into florets; discard stalks.
Cut red pepper into small pieces.
Cut green onions into 2-inch pieces.
Cut chicken into 1 inch pieces.
Set each ingredient aside separately.
Whisk together: 1/4 cup of the chicken stock, soy sauce, cornstarch, oyster sauce, sesame oil and chili paste; set aside.
Heat a wok or deep skillet over high heat until drop of water sprinkled on surface sizzles.
Pour in half of the oil and swirl wok to evenly coat side of pan; heat for 30 seconds. Add half of the chicken breasts, stir-fry chicken for 3 to 4 minutes or until no longer pink inside. Transfer to plate. Repeat with remaining chicken, adding more oil if necessary. Move chicken to plate.
Add remaining oil to wok. Stir-fry garlic and ginger for 10 seconds or until fragrant.
Add broccoli and red pepper; stir-fry for 1 minute.
Add onions; stir-fry for 30 seconds.
Pour in remaining 1/4 cup stock.
Cover and steam for 2 minutes or until broccoli is tender-crisp.
Return chicken to wok. Push contents of wok to side of pan.
Pour soy mixture into center of wok; cook, stirring, for 1 to 2 minutes or until thickened.
Stir vegetables and chicken into sauce until glazed and coated.
Sprinkle with nuts.
Remove to a serving platter or dish and serve immediately.