PREHEAT oven to 350°F. Heat 2 Tbsp. of the dressing in large skillet on medium-high heat. Add peppers, zucchini and onions; cook until crisp-tender, stirring occasionally. Add water; bring to boil. Stir in stuffing mix; cover. Remove from heat. Let stand 5 min.
MEANWHILE, place 2 of the chicken breasts in large freezer-weight resealable plastic bag. Pound chicken with the side of a heavy can, rolling pin or meat mallet until chicken is 1/4-inch thick. Remove chicken from bag; set aside. Repeat with remaining 6 chicken breasts, two at a time. Place chicken, top-sides down, on large cutting board. Spread evenly with stuffing mixture. Sprinkle each with 1 Tbsp. of the cheese. Starting at one of the short ends, tightly roll up each chicken breast. Place, seam-sides down, in 13x9-inch baking dish. Drizzle evenly with remaining dressing.
BAKE 30 min.; sprinkle with remaining 1/2 cup cheese. Bake an additional 5 min. or until cheese is melted and chicken is cooked through (170°F).