Patrick Swayze's Chicken Pot Pie

1 Whole chicken (3 1/2 lbs.)
1 Carrots; sliced thick
1 Rib celery; slick thick
1 md Onion; valved
10 c Water
1 Bay leaf
1/4 ts Fresh ground pepper
1/2 c Carrots; peeled, diced
½ c celery; diced
1 c Frozen pearl onions or 1 med. onion chopped
1 Red pepper; diced
8 oz Fresh mushrooms; quartered
1/2 c Frozen peas
3 tb Butter or margarine
3 tb All-purpose flour
1/2 c Milk
1 tsp Worcestershire sauce
1/2 tsp Salt & Pepper to taste
ds Red pepper sauce
1 pk pie crusts; thawed
1 lg Egg; lightly beaten

Combine chicken, sliced carrot and celery, the onion, water, bay leaf and pepper to large pot. Bring to boil. Reduce heat to low and skim surface. Simmer, partially covered, 1 hour, turning chicken after 30 minutes. Remove chicken. Cool; strain chicken broth and remove fat. Reserve 2 cups broth. Remove skin and bones from meat, tear into pieces. Transfer to bowl.
Bring reserved chicken broth to boil in large saucepan. Add diced carrots and celery; reduce heat and simmer 5 minutes. Add onions and red pepper; simmer 1 minute. Add mushrooms and peas; simmer 1 minute more. With slotted spoon or using a colander, transfer vegetables to chicken. Reserve broth.
Melt butter in medium saucepan over medium-high heat. Add flour and cook, whisking constantly, until golden brown. Whisk in reserved chicken broth and the milk, Worcestershire, salt and pepper sauce. Simmer 5 minutes, whisking occasionally. Add to chicken and vegetables and stir to combine.
Preheat oven to 425 degrees. Press bottom crust into pie pan and spoon in chicken mixture. Add top crust and flute edges. Brush with beaten egg. Bakes pot pie until top is golden and filling is bubbly, about 25-30 minutes.