Prepare the Chicken: If using a whole chicken, remove giblets and rinse. Pat dry. Season generously with salt and pepper. If using chicken thighs, season them as well.

Sauté Aromatics: In a large Dutch oven or stockpot, heat olive oil over medium heat. Add onion, carrots, and celery and cook until softened, about 5-7 minutes. Add garlic and cook for another minute until fragrant.

Brown the Chicken: If using a whole chicken, brown it on all sides in the pot. If using chicken thighs, brown them skin-side down first, then flip. Remove the chicken from the pot and set aside.

Build the Broth: Pour chicken broth into the pot, scraping up any browned bits from the bottom. Add bay leaves, thyme, and rosemary. Bring to a simmer.

Simmer the Chicken: Return the chicken to the pot. If using a whole chicken, ensure it's mostly submerged in the broth. Reduce heat to low, cover, and simmer for 1-1.5 hours, or until the chicken is cooked through and easily shreds. If using chicken thighs, simmer for 45-60 minutes.

Shred the Chicken: Remove the chicken from the pot and let it cool slightly. Shred the meat, discarding the skin and bones.

Prepare the Dumplings: While the chicken is cooling, make the dumplings. In a large bowl, whisk together flour, baking powder, and salt. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs.

Add Liquid: Gradually add milk (or buttermilk), stirring until just combined. Do not overmix! The dough should be slightly shaggy.

Cook the Dumplings: Drop spoonfuls of dumpling dough into the simmering broth, spacing them evenly. Cover the pot and simmer for 15-20 minutes, or until the dumplings are cooked through and fluffy. Resist the urge to lift the lid frequently, as this can cause the dumplings to deflate.

Combine and Serve: Return the shredded chicken to the pot. Stir gently to combine. Season with additional salt and pepper to taste. Garnish with fresh parsley before serving.