DEEP-DISH CHICKEN PIE

1 (5 lb) broiler-fryers, cut-up
4 cups water
2 teaspoons salt
1/2 tsp pepper
1/2 tsp marjoram leaves
2 large carrots, sliced
3/4 lb small white onions
1 celery large stalk, sliced
1 (10 oz) pkg frozen baby lima beans, thawed
1/2 lb small mushrooms
GRAVY:
1/2 cup all-purpose flour, divided
1 3/4 cups half-and-half, divided
1 1/2 teaspoons salt (or to taste)
PASTRY:
3 cups flour
1 cup plus 2 tbsp shortening
1/2 teaspoon salt
1/2 cup plus 1 teaspoon water, divided
1 egg yolk

CHICKEN:
In 5-quart Dutch oven or saucepot over high heat, combine chickens, 4 cups water, marjoram, 2 teaspoons salt, and pepper; bring to a boil. Reduce heat to low; cover and simmer 35 minutes or until chicken is fork-tender.

When chicken is done, remove chicken from broth and set aside to cool.

VEGETABLES:
Strain broth and place 1 cup of broth in a 3-quart saucepan (remaining broth may be refrigerated or frozen for another use). Add carrots, onions, and celery and bring to a boil over high heat. Reduce heat to low; cover and simmer 10 minutes or until vegetables are almost tender. Remove from heat. With slotted spoon, remove vegetables to medium-sized bowl. Add thawed lima beans and mushrooms. Set aside.

GRAVY:
In small bowl, blend 1/2 cup of the flour with 3/4 cup of the half-and-half; gradually stir into broth in saucepan; stir in remaining half-and-half. Over low heat, cook, stirring until sauce thickens slightly. Remove from heat.

When chicken is cool and easy to handle, remove and discard bones and skin. Cut meat into 1-inch pieces; stir into the gravy along with the vegetables and 1 1/2 teaspoon salt (or salt to taste). Spoon mixture into 13x9-inch baking dish.

Preheat oven to 350 degrees F.

PASTRY:
In medium-sized bowl, stir together the remaining 3 cups all-purpose flour and 1 1/2 teaspoon salt. With pastry blender or two knives used scissors fashion, cut shortening into flour to resemble coarse crumbs. Sprinkle about 1/2 cup water, a tablespoon at a time, into flour mixture, mixing lightly with a fork until pastry is just moist enough to hold together; shape pastry into a ball.

On lightly floured surface with floured rolling pin, roll two-thirds of dough into 15x11-inch rectangle. With knife, cut several small slits in center of pastry. Place pastry loosely over chicken mixture. Trim pastry edge, leaving 1-inch overhang; fold overhang under and press gently all around baking dish to make a high stand-up edge. Roll and cut remaining dough to make decorative design for top of pie.

In cup, beat egg yolk with 1 teaspoon water. Brush pastry with egg-yolk mixture.

TO BAKE:
Bake pie in 350 degree F oven 1 hour or until crust is golden and chicken mixture is heated through.