In a sauce pan over medium-high heat, add chicken, and broth. Cook for 10 minutes.
Preheat oven to 400degF. Slice a third of the potatoes into thin chips, dice the rest of them.
Remove chicken from broth, reserve the broth. Chop up chicken into small pieces.
In another sauce pan, add butter, tarragon, thyme, one teaspoon of salt and one teaspoon of pepper. Once melted, whisk in flour and cook for 3 minutes. The whisk in reserved chicken broth.
In a 13x9 baking dish, combine diced potatoes, cut up chicken, garlic, onions, peas , carrots and gravy. Arrange sliced potatoes in a single layer (with slight overlap) to cover entire baking dish. Sprinkle with remaining salt and pepper.
Cover with foil and put in oven for 25 minutes. Remove foil and bake another 15 minutes. Let rest for at least 5 minutes before serving.