In a large saucepan, melt margarine over medium low heat and saute onion. When onions are translucent, add flour, salt, and pepper and stir constantly for at least one full minute to ensure the starchy taste is cooked off.
Slowly add broth and milk, stirring and scraping the bottom of the pan as the liquid thickens. Continue to heat on low, allowing the full mixture to simmer for one minute.
Stir in the chicken and vegetables and set pan aside.
Preheat oven to 425°
Prepare pastry by combining shortening, flour, celery seed, and salt, fully incorporating with a fork or pastry cutter.
Place a few ice cubes in a cup of water and spoon out 2-3 tablespoons of water into the mixture and stir, continuing to add water a tablespoon at a time until the dough forms a ball.
Roll 2/3 of dough with a rolling pin into a circle and ease it into a pie plate. Pour chicken filling in.
Roll remaining dough into a circle to place over the filling. Pinch edges, ensuring all dough is around the pie plate edge.
Brush with a beaten egg for a glistening, brown crust
Place pie plate on a baking sheet and bake at 425° 30 to 35 minutes until crust is brown.