Wash the chicken and giblets under cold water. Place in a large kettle with quartered onion, celery, parsley, 2-1/2 teaspoons salt, the black peppers, bay leaf and 2 cups eater. Bring to boil, reduce heat, and simmer for 1-1/2 hour or until chicken is tender. Remove chicken; cool. Chop giblets fine. Remove chicken from bones in large pieces. Strain stock, skim off gar, and measure out 4 cups, if more is needed add water.
Add the stock to medium saucepan, cook carrots, potatoes, and onion. Covered, 20 minutes or until tender. Remove vegetables with a slotted spoon and set aside.
In a small bowl, combine flour, salt and pepper. Stir in milk until smooth. Add to stock in pan; bring to boil, stirring. Reduce heat; simmer, 8 min, or until sauce is thick. Add chicken, vegetables and giblets. Turn into a round 3 quart casserole.
Preheat oven to 450º. Prepare the piecrust according to directions, adding ¾ teaspoon dried thyme leaves to flour mixture. Form pastry into a ball. On a lightly floured pastry surface, roll out pastry to corm a circle ½” larger than top of casserole, turning edges under, crimp, pressing to rim of casserole to seal. With a serrated knife, make 5 or 6 slits for air vents, evenly dispersed in top of pastry. Brush surface of pastry evenly with melted butter. Bake 35-40 min or until crust is golden and the mixture bubbles through the slits.