Pat the Chicken Thighs dry and season generously with Kosher Salt and Black Pepper.
Heat a large Dutch oven or heavy pot over medium-high heat and add Butter. When it’s hot, brown the chicken thighs in batches, 4–5 minutes per side, until nicely golden; transfer the browned pieces to a plate and set aside.
Reduce the heat to medium, add another tablespoon of butter if needed, then add the Onion, Carrot and Celery. Cook, stirring occasionally, until the vegetables are softened, about 5–7 minutes. Add the Garlic and cook 30–60 seconds more until fragrant.
Sprinkle in the All-Purpose Flour and cook, stirring, for 1–2 minutes to eliminate the raw flour taste and form a light roux.
Slowly pour in the Chicken Broth and a cup of Water, scraping up any browned bits from the bottom of the pot. Add the Thyme and Bay Leaf, then return the browned chicken to the pot. Bring to a simmer, cover, and cook gently for 25–30 minutes, until the chicken is cooked through and tender.
Remove the chicken to a board, shred or chop it, discarding bones and skin as desired, and return the meat to the pot. Taste the broth and adjust seasoning with more salt and pepper if needed.
Meanwhile, make the dumpling dough: in a medium bowl combine 2 cups All-Purpose Flour (the same All-Purpose Flour used above), Baking Powder, and a pinch of Kosher Salt. Cut cold Butter into the dry ingredients until the mixture resembles coarse crumbs. Stir in Whole Milk and fold in chopped Parsley until just combined—the dough should be soft and scoopable.
Bring the stew to a gentle simmer (not a rolling boil). Drop the dumpling dough by rounded tablespoons onto the surface of the simmering broth, spacing them so they don’t touch. Cover tightly and simmer for 12–15 minutes without lifting the lid, until the dumplings are puffed and cooked through.
Stir in the Heavy Cream to enrich the broth, warm through for a couple of minutes, then remove the bay leaf and adjust seasoning. Serve hot, garnished with more chopped Parsley if you like.
