Heat oven to 375°F. On lightly floured surface, unroll puff pastry. With rolling pin, roll out into 11-inch square. Cut off corners to make an 11-inch round. Cut slits or small designs in several places in pastry; set aside.
In 10-inch skillet, heat oil over medium-high heat. Add chicken; cook about 4 minutes, stirring frequently, until no longer pink in center. Add onion and carrots; cook 5 minutes, stirring frequently, until vegetables are crisp-tender. Remove from heat; stir in peas.
In medium bowl, beat remaining ingredients except egg with wire whisk until well blended. Stir into chicken mixture in skillet. Spoon into 9-inch deep-dish glass pie plate. Place pastry over filling allowing to hang over edge.
Bake 20 minutes. Brush crust with beaten egg. Cover edge of crust with strips of foil to prevent excessive browning.
Bake 20 to 25 minutes longer or until crust is golden brown. Let stand 10 minutes before serving.