Preheat oven to 400 degrees F. In a large saucepan melt butter over medium heat. Stir in flour. Cook and stir for 1 minute. Stir in broth and the 1 1/2 cups milk. Cook and stir until slightly thickened and bubbly. Stir in chicken, vegetables, onions, poultry seasoning, salt, and pepper. Cook and stir until heated through. Set aside; keep warm.
Prepare Pastry Topper for Pot Pie. On a lightly floured surface, roll pastry from center to edges into an oval or rectangle 1 inch larger than a 3-quart oval or rectangular baking dish (about 14x10-inches). Transfer hot chicken mixture to baking dish. Cut pastry into 1 1/2-inch-wide strips. Weave strips over hot filling in a wide lattice pattern. Trim pastry 1/2 inch beyond edge of dish. Brush top of pastry with the 1 tablespoon milk. Sprinkle with Parmesan cheese.
Bake about 40 minutes or until light brown and edges are bubbly. Let stand for 10 minutes before serving. If desired, sprinkle with parsley.
Pastry Topper for Pot Pie
In a large bowl stir together flour and salt. Using a pastry blender, cut in shortening and butter until pieces are pea-size.
Sprinkle 1 tablespoon of the water over part of the flour mixture; toss with a fork. Push moistened pastry to side of bowl. Repeat moistening flour mixture, using 1 tablespoon of the water at a time, until flour mixture is moistened. Gather flour mixture into a ball, kneading gently until it holds together.