In the bottom of a large heavy bottomed pot or Dutch oven, melt the butter. Add diced onion, sliced carrots and celery. Season with salt and black pepper to your taste. Cook for 5-8 minutes over medium-high heat, until the vegetables are beginning to soften and brown.
Add 1/4 cup all-purpose flour stirring to coat the vegetables.
To the pot add bay leaf, canned soup, chicken stock or broth, chopped chicken, poultry seasoning, garlic powder, onion powder and tarragon. Taste and adjust the salt and black pepper to your taste. Stir well.
Increase the burner temperature and bring to a boil.
Meanwhile, in a medium sized mixing bowl, mix together the buttermilk baking mix and buttermilk until a sift dough forms.
Using a Tablespoon or 1 1/2 ounce (medium) ice cream scoop divide the dumpling dough dropping into the boiling broth.
After all of the dumpling dough has been added, place the lid on top and turn the heat to low. Cook simmering gently. Do not lift the lid for 20 minutes.
After 20 minutes, uncover the pot and use a large spoon to gently press the dumplings into the broth.
Remove from the heat. Allow to rest uncovered for 5 minutes before serving.
Stir the dumplings through the broth just before serving. (This will naturally thicken the broth.)
Special Note: To thicken the broth further, remove the dumplings to a platter and keep warm. Bring broth to a simmer. Dissolve 2-3 Tbsp flour in cold water or milk, and whisk into the broth. Repeat until you reach your desired consistency. Return the dumplings to the pot and stir before serving.