Rinse the chicken and pat dry. Season with 1 tablespoon salt and pepper. Add 2 tablespoons of the oil to a large stockpot over high heat. Add the chicken pieces and lightly brown evenly, removing and adding as necessary. Once all of the chicken is browned, add ingredients through smashed garlic. Brown the vegetables over high heat for 5 to 6 minutes, then add in the water, peppercorns, savory and bay leaf and bring to a boil. Reduce the heat to a strong simmer and after 20 minutes, check the chicken pieces, removing as they finish cooking. Remove the chicken, to a cutting board and cool until you are able to handle, then the strip meat and put bones back into pot.
Simmer the stock and bone mixture, uncovered, for 45 minutes. Strain and adjust seasoning with additional salt, if needed. Chop the meat, discarding any skin, ligament or fat as you go and set aside.
In a separate saute pan over medium heat, add the remaining 2 tablespoons of oil and diced vegetables. Saute until the onion is translucent, about 5 minutes, then add the garlic and red chili flakes and saute for 1 minute more. Add the vegetables to the strained chicken stock, then in the same saute pan, add the butter. When melted, add the flour and stir constantly for 2 minutes. Slowly ladle in some of the hot stock, whisking as you add, until approximately 2 cups of stock have been added. Add the roux mixture back into the stock pot and combine well. Add the cream and the chicken back into the stock pot and keep at a low simmer while you prepare the dumplins.
In a large bowl, combine the dry ingredients. In a separate medium, nonreactive bowl, combine the wet ingredients, adding the melted butter last.
Pour the wet ingredients into the dry ingredients and with a rubber spatula, very gently, fold together until just combined.
Using 2 dinner spoons, shape the dough into golf ball-size, quenelle shaped biscuits and drop them into the hot soup. Cover with a tight fitting lid and allow the dumplins to cook for 15 to 20 minutes over low heat.
Ladle into soup bowls and serve hot.