Combine chicken broth, celery, carrot, onion, garlic cloves, peppercorns, bay leaves, and dried thyme in a large pot to create a flavorful base for the stew.
Add chicken breast to the broth mixture, ensuring it's fully submerged.
Bring the pot to a boil, then reduce heat and simmer until the chicken is thoroughly cooked and tender, about 15 minutes.
Meanwhile, mix the 3 cups of all-purpose flour, baking powder, and kosher salt in a bowl for the dumplings. The dough should be shaggy but still easily form a ball.
Stir in 1 cup of milk to form a soft dough, knead it into a ball, wrap it in plastic wrap, then let the dough rest while the meat is cooking. Add more milk as needed for the dough ball to come together.
Once the dough has rested for about 15 minutes, turn it out onto a very lightly floured counter and roll it out until it’s about ⅛-inch thick. Cut it into squares.
Remove the chicken from the pot and set it aside to cool for a bit until it can be safely handled.
Strain the broth to remove the vegetables and spices, returning the clear broth to the pot.
Cook dumplings in the broth until they are puffed up and cooked through, about 15 minutes.
Return the shredded chicken to the pot, season with salt and pepper to taste, and stir gently to combine everything evenly.
Make a slurry combining the reserved 1/4 cup of flour with about 1/2 cup of water or chicken broth.
Drizzle the slurry slowly into the simmering stew while stirring. Simmer until thickened. Adjust the salt and pepper to taste.
Serve hot, with a sprinkle of fresh herbs if desired, for added flavor.