Step 1

Melt butter in a stock pot over medium-high heat. Add celery, carrot, onion, garlic, bay leaves, thyme, salt, pepper, and poultry seasoning; cook and stir until flavors combine, about 5 minutes. Push vegetable mixture to the sides and add chicken; cook until browned, 3 to 5 minutes per side.

Step 2

Pour enough water over the chicken to cover by 3 inches; bring to a boil. Stir, scraping the browned bits off of the bottom of the pot. Reduce heat; simmer until chicken is tender, about 1 hour. Transfer chicken and carrots to a serving plate with a large slotted spoon; let cool.

Step 3

Ladle 1/4 cup cooking liquid into a bowl; cool slightly, about 5 minutes. Mix in 2 tablespoons flour. Stir back into the pot.

Step 4

Place 2 cups flour in a large bowl; cut in shortening with 2 knives until mixture forms pea-sized bits. Mix in chilled chicken broth until dough is combined.

Step 5

Turn dough out onto a floured work surface. Knead 5 to 6 times; pat down to 1-inch thickness. Sprinkle lightly with flour; roll out to about 1/8-inch thickness. Cut dough into squares with a sharp knife.

Step 6

Drop squares, in batches, into simmering cooking liquid, moving squares to the side with each addition. Partially cover pot; simmer until dumplings are firm, about 12 minutes. Separate any dumplings that stick together. Remove from heat; keep covered.

Step 7

Bone chicken; cut into bite-sized pieces and return to the pot. Chop carrot; return to the pot. Cool chicken and dumplings, about 30 minutes, before serving.