Melt butter or margarine in heavy kettle or Dutch oven; brush part on inside of chicken, then sprinkle chicken with 1 teaspoon thyme.
Brown chicken lightly on all sides in remaining butter or margarine.
Turn chicken, breast side up; pour beef broth over; sprinkle with remaining 1 teaspoon thyme; cover tightly.
Simmer, basting a few times with pan juices, 1 1/2 hours, or until tender.
Remove to heated serving platter; keep hot while making gravy.
Pour broth from kettle into 4 cup measure.
Let fat rise to top, then skim off.
Add water to broth, if needed, to make 2 1/2 cups.
Return 2 tablespoons fat to kettle; blend in flour; stir in broth.
Cook, stirring constantly, until gravy thickens and boils 1 minute.
Blend in evaporated milk; heat just to boiling.
Serve chicken with buttered noodles and spoon gravy over all.