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HEAT oil in large deep skillet on medium-high heat. Add chicken; cook and stir 4 min. or until no longer pink. Transfer to bowl.
ADD broth gradually to flour in small bowl, whisking constantly until blended. Add to skillet; cook and stir on medium heat 2 min. or until thickened. Add cream cheese spread; cook and stir 3 min. or until melted. Remove from heat; stir in chicken and vegetables.
STIR baking mix, sour cream and milk just until baking mix is moistened. Spoon into 6 mounds over mixture in skillet; cook on medium-high heat 2 min. Cover skillet; cook on low heat 15 min. or until chicken is done and toothpick inserted in dumplings comes out clean.
TOP with Parmesan and parsley.