Preheat oven to 400°.
Bring broth to a boil in a large Dutch oven. Add peas and next 5 ingredients (through onions) to pan; cover, reduce heat, and simmer for 6 minutes. Add chicken; cook for 5 minutes or until chicken is done. Remove chicken and vegetables from broth with a slotted spoon; place in a large bowl.
Increase heat to medium. Lightly spoon flour into dry measuring cups; level with a knife. Place all but 1 tablespoon flour in a medium bowl; gradually add milk to bowl, stirring with a whisk until well blended. Add milk mixture to broth; cook for 5 minutes or until thickened, stirring frequently. Stir in chicken mixture, parsley, thyme, salt, and pepper. Spoon mixture into an 11 x 7-inch baking dish coated with cooking spray.
Sprinkle remaining 1 tablespoon flour on a work surface; roll dough into a 13 x 9-inch rectangle. Place dough over chicken mixture, pressing to seal at edges of dish. Cut small slits into dough to allow steam to escape; coat dough lightly with cooking spray. Place dish on a foil-lined baking sheet. Bake at 400° for 16 minutes or until pastry is browned and filling is bubbly.