In a large pot, combine the chicken, chopped onion, sliced carrots, and sliced celery. Pour in the chicken broth and bring to a simmer over medium heat. If using a whole chicken, verify it's fully submerged. Simmer for 45-60 minutes until the chicken is tender and fully cooked.
Once the chicken is cooked, carefully remove it from the pot and let it cool slightly. Strain the broth to remove the vegetables and return it to the pot.
If you prefer a thicker broth, make a roux by melting 1/4 cup of butter in a separate pan, mixing in 1/4 cup of flour, and then whisking it into the strained broth. Alternatively, you can mix cornstarch with water and add it to the broth to thicken.
Season the broth with salt, black pepper, thyme, and bay leaves to taste. If desired, stir in heavy cream or evaporated milk for an extra creamy texture.
To prepare the dumplings, in a mixing bowl, combine 2 cups of flour, baking powder, and salt. In a separate bowl, mix melted butter (or shortening) with milk, then combine with the dry ingredients until just mixed. Drop dumplings are steamed while infused with the soup's rich liquid.
Drop spoonfuls of the dumpling batter into the simmering broth. Cook uncovered for 15-20 minutes until the dumplings are cooked through and fluffy. Avoid overcrowding the pot with dumplings, as this can affect their cooking.
While the dumplings are cooking, shred the chicken and return it to the pot once the dumplings are done. Stir gently to combine and allow to heat through.
Serve the chicken and dumplings immediately, garnished with fresh parsley. Enjoy with a simple green salad and some fruit for a complete meal.
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