Preheat oven to 425°F (220°C). Generously season chicken with salt and pepper.
Add oil to large room-temperature skillet. Add chicken. Place skillet over medium heat and cook. Allow meat to brown, and pour off excess fat to keep only a thin layer in pan until chicken is cooked halfway through, about 10 minutes.
Transfer skillet to oven. Roast until chicken is cooked through and skin is crisp, about 6 to 8 minutes.
Transfer chicken from skillet to platter. Return skillet to medium heat. Add shallot and garlic; cook, stirring frequently, until fragrant, about 1 minute. Whisk in Dijon mustard, apple cider, broth and a bit more salt and pepper; cook for about 3 minutes.
Return chicken to skillet along with juices that have settled on platter to rewarm. Serve with your favourite sides.