Cook meat in a large skillet over medium heat until browned, stirring occasionally. Drain well, and set aside.
Sauté onion in butter in a large skillet until tender; add cooked meat, parsley, salt, thyme, and pepper, stirring well. Combine beef broth and flour; stir well. Add broth mixture to meat mixture, stirring well. Cook over low heat, stirring frequently, until slightly thickened.
Line a 9-inch pie plate with half of pastry. Pour meat mixture into pastry shell. Cover with top crust. Trim edges of pastry; seal and flute edges. Cut slits in top for steam to escape. Bake at 350° for 1 hour or until crust is golden brown.