In a bowl, combine 1/2 cup of all-purpose flour, salt, and freshly ground pepper. Mix well to season the flour.
Take the cut-up chicken and coat each piece in the seasoned flour mixture. Shake off excess flour.
In a Dutch oven over medium heat, add 2 tablespoons of oil. Brown the floured chicken pieces in the Dutch oven. Be cautious not to cook them entirely, just brown the exterior for flavor. Once browned, remove the chicken from the Dutch oven and set aside.
Sprinkle the remaining 1/4 cup of flour over the sautéed vegetables. Stir to incorporate the flour, creating a roux.
Gradually add chicken stock, stirring continuously to avoid lumps. Add apple cider, sugar, bay leaves, and whole peppercorns. Allow the mixture to come to a simmer.
Once the mixture is simmering, add the browned chicken back to the Dutch oven. Simmer the soup for about 25 minutes, allowing the flavors to meld.
In a separate bowl, combine 1-1/3 cups of all-purpose flour, baking powder, and salt. In another bowl, mix together milk and melted butter. Pour the wet ingredients into the dry ingredients and stir until just combined.
Take spoonfuls of the dumpling dough and drop them onto the simmering soup. Cover and let the dumplings cook for about 15 minutes or until they are cooked through.
While the dumplings are cooking, shred the chicken using two forks. Set aside the shredded chicken.
Once the dumplings are cooked, add heavy whipping cream, parsley, and thyme to the soup. Gently stir in the shredded chicken. Season with additional salt and pepper to taste.
Ladle the Chicken and Dumplings into bowls. Garnish with additional herbs if desired. Serve hot and enjoy your comforting and flavorful Chicken and Dumplings!