1 (4-pound) whole chicken
10 cups water
4 cups unsalted chicken stock
1 tablespoon black peppercorns
3 celery stalks, coarsely chopped (about 6 ounces)
2 carrots, cut into 1-inch pieces (about 5 ounces)
2 bay leaves
1 onion, peeled and cut into wedges (about 10 ounces)
1/2 bunch fresh flat-leaf parsley (about 2 ounces)
Soup and Dumplings:
3 tablespoons butter, divided
1 cup chopped onion
1/4 cup sliced celery
1 carrot, halved lengthwise and sliced
1 tablespoon all-purpose flour
1 teaspoon kosher salt, divided
1/2 teaspoon freshly ground black pepper
4.5 ounces all-purpose flour (about 1 cup)
1 teaspoon baking soda
6 tablespoons nonfat buttermilk
1 tablespoon chopped fresh thyme
3 tablespoons chopped fresh flat-leaf parsley
To prepare stock, remove giblets and neck from chicken; trim excess fat. Place chicken, 10 cups water, and next 7 ingredients (through parsley bunch) in an 8-quart stock pot. Bring to a boil; reduce heat, and simmer, uncovered, 1 hour, skimming foam from surface as necessary. Remove from heat; let stand 20 minutes.
Remove skin from chicken; remove chicken from bones, discarding skin and bones. Shred chicken with 2 forks into bite-sized pieces. Strain broth through a sieve into a large bowl; discard solids. Cool broth and chicken to room temperature. Cover and chill broth and chicken 8 to 24 hours. Skim solidified fat from surface; discard. Reserve 8 cups of the broth and all of the chicken. Refrigerate remaining broth in an airtight container for up to 1 week, or freeze for up to 3 months for another use.
To prepare dumplings, melt 1 tablespoon butter in a Dutch oven over medium heat. Add onion, celery, and carrot to pan; cook 8 minutes, stirring occasionally. Stir in 1 tablespoon flour, 3/4 teaspoon salt, and pepper; cook, stirring constantly, 1 minute. Stir in 8 cups reserved stock. Bring to a boil; reduce heat and simmer 15 minutes, stirring occasionally.
Weigh or lightly spoon 4.5 ounces flour (about 1 cup) into a dry measuring cup; level with a knife. Combine flour, baking soda, and 1/4 teaspoon salt, stirring with a whisk. Cut in 2 tablespoons butter with a pastry blender or 2 knives until mixture resembles coarse meal. Add buttermilk, stirring until moist.
Drop dough in 24 (about 1-teaspoon) portions into broth mixture. Cover and cook 8 minutes. Gently stir in reserved shredded chicken and thyme. Simmer very low 6 minutes or until thoroughly heated and dumplings are done. Remove from heat, and ladle into shallow bowls. Sprinkle evenly with chopped parsley.