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1
Prepare Chicken: Preheat oven to 350u00b0. If chicken has giblets, remove them, and reserve for another use. Rinse chicken, and pat dry. Place chicken in a 13- x 9-inch baking dish, breast side up; brush entire bird with oil, and sprinkle with salt and pepper. Bake at 350u00b0 for 1 hour and 10 minutes or until a meat thermometer inserted into thickest portion of thigh registers 165u00b0. Cool 30 minutes. Remove chicken skin and bones, and reserve them for stock. Shred meat with two forks, or coarsely chop. Set aside.
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2
Prepare Dumplings: Whisk eggs in a large bowl. Add melted butter and salt, whisking until smooth. Gradually add flour, stirring until mixture forms a ball. Turn dough out onto a lightly floured surface, and roll into a 12-inch square on a lightly floured surface. (Dough should be about 1/4 inch thick.) Let dough rest, uncovered, 10 minutes. Cut dough into 2-inch squares. Place dumplings on a large parchment paper-lined baking sheet. Cover and chill until ready to cook.
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3
Prepare Stock: Bring 8 cups water and reserved chicken skin and bones to a boil in a 6-qt. Dutch oven. Remove from heat; strain stock into a large bowl. Discard skin and bones. Return stock to Dutch oven. Add onion and next 4 ingredients; bring to a boil. Add dumplings to boiling stock. Reduce heat to medium; cover and cook for 30 minutes, stirring often.
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4
Prepare Roux: Melt butter in a 2-qt. saucepan over medium heat. Whisk in flour until smooth. Cook 10 minutes or until light brown, stirring constantly.
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5
Stir roux and shredded chicken into stock; reduce heat to medium-low, and cook, uncovered, 20 minutes or until thickened, stirring often. Season with additional celery salt, if desired.
