BRING water to boil in large skillet. Add broccoli; cover. Simmer on medium-low heat 5 min. or until crisp-tender. Meanwhile, mix 2 Tbsp. dressing, peanut butter, soy sauce, Sriracha sauce and pepper until well blended; set aside. Cut 3 green onions into 1-inch pieces; thinly slice remaining onion.
REMOVE broccoli from skillet; cover to keep warm. Heat remaining dressing in skillet on medium-high heat. Add garlic and ginger; cook and stir 1 min. Add chicken; cook 2 min., stirring frequently. Stir in peanut butter mixture, 1-inch onion pieces and pineapple; cook 5 to 7 min. or until chicken is done and sauce is thickened, stirring frequently to scrape up browned bits from bottom of skillet.
TRANSFER chicken mixture to serving plate; top with sliced onions. Surround with broccoli.