Cook chicken: Combine first 7 ingredients in a large Dutch oven; bring to a boil. Cover, reduce heat, and simmer 1 hour or until chicken is tender. Remove chicken, reserving broth in Dutch oven; discard vegetables and bay leaf. Let chicken cool; skin, bone, and cut into bite-size pieces.

Cook vegetables: With a large spoon, skim fat (oily liquid) from surface of broth reserved in Dutch oven; bring broth to a boil. Add frozen vegetables and potatoes; return to a boil. Reduce heat, cover, and simmer 8 minutes or until tender. Remove vegetables from broth, and set aside. Measure 3 cups broth; set aside. Reserve remaining broth for other uses.

Make sauce: Melt butter in Dutch oven over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add 3 cups broth and milk; cook over medium heat, stirring constantly, until mixture is thickened and bubbly. Stir in 1½ teaspoons salt, 1¼ teaspoons pepper, and thyme. Add vegetables, chicken, and hard-cooked eggs; stir gently. Spoon into a lightly greased 13- x 9- x 2-inch baking dish; set aside.

Build and bake pot pie: Roll out piecrust on a lightly floured surface into a 15- x 11-inch rectangle (piecrust will be very thin). Place over chicken mixture; crimp edges, pressing against sides of baking dish. Cut slits in top for steam to escape; bake at 400° for 20 minutes or until golden brown.