In a large stock pot or Dutch oven, bring 1 ½ teaspoons of oil over medium heat. When the oil is heated, add the chicken breasts to the pot in a single layer. Lightly season with salt and pepper. Let the chicken cook, flipping once, until the outsides are browned and the center is almost or just cooked through. Remove chicken to a plate and set aside.

Add the remaining 1 ½ teaspoons of oil to the pot and add the onions, carrots and leeks. Allow the vegetables to cook until softened, about 7 minutes. Stir the flour into the vegetables until coated. Add the wine, broth, milk, thyme and bay leaf. Shred chicken breasts into small pieces (or chop) and add the chicken to the pot as well. Stir to combine and reduce heat to medium-low. Cover the pot and simmer for 30 minutes. After the 30 minutes, uncover and add the tarragon, salt & pepper.

While the stew is simmering, mix together the flour, baking powder and salt for the dumplings in a large bowl. In a separate bowl, combine the milk and butter and microwave until just warmed (butter should be just melted), 1-2 minutes. Add the milk mixture to the flour mixture in the large bowl and stir together until thoroughly combined. Mix in the tarragon, parsley and chives.

When the stew is done cooking, drop spoonfuls of the dumpling dough into the pot forming 16 large dumplings (or 24 smaller dumplings if you prefer). Reduce the heat to low and cover the pot. Cook for 15-18 minutes until the dumplings puff up and double in size. Dunk dumplings to coat with the stew and serve.