Prepare the Dumpling Dough: In a medium bowl, whisk together 2 cups of flour, baking powder, 1 teaspoon salt, and 1/2 teaspoon pepper. Cut in the 4 tablespoons of cold, cubed butter using your fingertips or a pastry cutter until the mixture resembles coarse crumbs. Stir in the buttermilk or milk until a shaggy dough forms. Do not overmix. Turn the dough onto a floured surface, knead gently 3-4 times, then cover with plastic wrap and let it rest.

Sear Chicken & Sauté Aromatics: Pat chicken thighs dry and season generously with salt and pepper. Heat olive oil in a large Dutch oven over medium-high heat. Sear chicken for 3-4 minutes per side until golden brown; remove and set aside. Reduce heat to medium, add the stick of butter, then sauté the onion, carrots, and celery for 6-8 minutes until softened.

Create the Velvety Broth: Sprinkle 1/2 cup of flour over the vegetables and cook, stirring constantly, for 2 minutes. Slowly pour in the chicken broth, whisking constantly to prevent lumps. Stir in the dried thyme, bay leaves, and another pinch of salt and pepper.

Simmer the Chicken: Return the seared chicken and any accumulated juices to the pot. Bring to a simmer, then reduce heat to low, cover, and cook for 20-25 minutes until the chicken is tender. Remove the chicken, shred it with two forks, and set aside. Stir the heavy cream or milk into the broth, then return the shredded chicken to the pot. Adjust seasoning if needed.

Roll and Cut the Dumplings: On a well-floured surface, roll the rested dough to about 1/4-inch thickness. Using a pizza cutter or knife, cut the dough into 1-inch wide strips, then cut the strips into 2-inch long rectangles.

Cook the Dumplings: Bring the stew to a steady, gentle simmer. Drop the dumplings one by one into the stew. Cover the pot tightly, reduce heat to low, and cook undisturbed for 15-18 minutes. Do not lift the lid. The dumplings are done when they are firm and tender.

Serve: Ladle the chicken and dumplings into warm bowls and garnish generously with fresh parsley.