Preheat the Oven to 325℉.
Gather all of your ingredients, Dutch oven, cutting board and chef's knife.
Season the chicken thighs generously with salt and pepper on both sides. Set aside while you prepare the vegetables.
Peel and cut your onions into large chunks, then set aside.
Prepare the carrots by peeling the outer layer, removing the stems and cutting on the bias into even pieces.
Peel the outer layer of your head of garlic and separate out each clove. Carefully using your Chef's knife, trim the ends of each clove, and holding the knife down on the papery outer skin, pull the garlic clove away and out. Peel away any remaining attached skin. Carefully using your Chef's knife, trim the ends of each clove, and holding the knife down on the papery outer skin, pull the garlic clove away and out. Peel away any remaining attached skin and set aside your peeled garlic. Place your Dutch oven over medium high heat and add 2 Tablespoons of olive oil.
Once the oil is hot, you're ready to add the chicken, skin side down first. Sear for about 5 minutes per side, just to get a golden-brown color on the outside. Once you've placed your chicken down, just leave it alone until it's ready to flip. Once that seared crust has formed, the chicken will be easier to rotate; otherwise, you risk tearing the skin.Once the chicken has been seared, remove the chicken from the pan, and set aside. Using a wooden spoon, scrape up any of the tasty bits on the bottom of the pan.
Add your vegetables and garlic, mixing thoroughly with a wooden spoon to coat all of the ingredients with the oil and pan drippings from the chicken. Season with salt and pepper.
Add in the chicken stock and white wine and stir.
Toss in the whole sprigs of thyme, and add the chicken back into the pot, skin side up.
Bring to a full boil, then cover the Dutch Oven with its lid, and move the whole pot directly into the preheated oven. Braise for 2-½ hours.
During the last hour of cooking, prepare the whipped potatoes for which the braised chicken will be served with. You can follow the recipe here. Hold potatoes warm. After braising, remove the Dutch oven from the oven, and using a pair of tongs, carefully remove chicken and place directly onto your serving platter or individual plates. Chicken will be incredibly tender, with the meat easily falling off the bone.
Serve chicken atop prepared whipped potatoes with a side of the braised carrots (feel free to serve the onions if you wish, but I typically don't!) Spoon some of the braising liquid over the top of the dish and serve immediately.