To make the filling, place the chicken in a large pot and cover with water. Add teh onion, carrot, celery, parsley, and 1 t salt, if needed. Season to taste with additonal salt and pepper. Siimmer over low heat for 1 1/2 hours, or until the chicken is very tender. Let cool.
Remove the chicken from the bones and discard teh bones and skin. Strain the broth, skim off the fat, and discard the solids. Refrigerate the fat for later. You will need 3 cups of broth; freeze the rest for another use.
In a shallow dish, pour 1 1/2 cups of broth over the chicken meat and set aside.
Melt the butter with 2 T of reserved chicken fat in a med saucepan over med heat. Stir in the flour and heat until thick and smooth, about 2minutes. Stir in the remaining 1 1/2 cups broth and continue stirring until the sauce is smooth and thick. Stir in the cream and frozen vegetables and keep warm.
To make the pastry, sift together the flour, salt, and baking powder in a med bowl. Cut in the butter and shortening (or use the reserved chicken fat) with 2 knives or rub in with your fingers. Add the milk a little at a time. Add just enough to hold the dough together. Divide the pastry in half and roll each into a large circle big enough for a 10-inch pie pan.
Preheat the oven to 400°F.
Transfer one dough circle to the pie pan, allowing the dough to overhang the edges. With a slotted spoon, remove the chicken from its broth and place in the bottom of the pie. Pour the cream sauce over it and cover with the top pastry round. Poke a few steam holes with a knife, pinch together the top and bottom pastries, and crimp the edges.
Bake for 25 minutes, or until the top is golden brown.
Let stand for 10 minutes. Cut into wedges and serve hot.