Place a large pot or Dutch oven over medium high heat and add oil. Once the oil is hot add the onion, carrots and celery and saute for 5 minutes. Add the garlic about halfway through so that it doesn't burn.
Add the chicken, chicken broth and the herbs to the pot and bring to a simmer. Simmer for 20 minutes or until the chicken is cooked all the way. (Chicken is cooked when juices run clear)
While the broth is simmering, combine everything for the dumplings in a medium-sized bowl.
In another medium-sized bowl mix 2 cups of flour and 2 1/2 cups milk to make a slurry. This will thicken the broth.
Remove the chicken from the pot and slowly add the slurry mix. Stir continuously.
Once all the slurry is added, bring the mixture back to a simmer and begin dropping in the dumplings.
Cover for 20 minutes.
Add the chicken back to the pot and stir gentle and serve.