Preheat an oven to 350 F.
Prep the chicken. Pat the chicken very dry and then season all over with salt and pepper. Lay them on a plate or tray, skin-side up and transfer to the fridge uncovered for 4-8 hours.
Sear the chicken. Heat the oil in a braiser or large oven-safe skillet over medium heat. Once the oil is hot, place the chicken in the skillet skin-side down. Reduce the heat to medium-low and brown the chicken for 8-10 minutes, until the skin is very golden brown. Flip the chicken and cook for 2 minutes, then transfer to a plate. Remove all but 1 tablespoon of fat from the skillet.
Sear the shallots. Add the butter to the skillet and increase the heat to medium. Once the butter is melted and foamy, add the halved shallots, cut side down, and cook for 3-4 minutes until browned. Transfer the shallots to the plate with the chicken.
Build the pan sauce. Add the sliced garlic and thyme leaves to the skillet and cook for 1 minute, until fragrant. Sprinkle in the flour and stir well. Cook the flour for 2-3 minutes, stirring constantly, and then stir in the wine. Bring to a gentle simmer and stir in the dijon and apple cider. Bring to a gentle simmer until the sauce thickens. Season to taste with salt and lots of cracked black pepper.
Braise the chicken. Nestle the chicken, skin-side up, into the sauce along with the shallots. Cover and transfer to the oven. After 30 minutes, remove the lid and continue cooking for another 35 minutes. Check the internal temperature to ensure that it’s reached at least 165 F.
Serve. Remove the skillet from the oven and let the chicken rest for 10 minutes. Garnish with more thyme leaves and serve over mashed potatoes, rice, or buttered noodles.