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Arrange a rack in the middle of the oven and heat the oven to 350°F.
Smash 2 garlic cloves and place in a small saucepan. Add 1 cup apple cider, 1 fresh rosemary sprig, and 1/4 teaspoon Dijon mustard. Stir and bring to a boil, uncovered, over medium-high heat. Boil until reduced to 1/4 cup, 15 to 20 minutes. Meanwhile, start cooking the chicken.
Pat 2 pounds chicken thighs dry with paper towels, then season with 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper.
Heat 2 teaspoons vegetable oil in a large frying pan or cast iron skillet over medium-high heat until it shimmers. Place the chicken skin-side down, and cook undisturbed until the skin is browned and the chicken releases easily from the pan, adjusting the heat if the skin begins to burn, 8 to 10 minutes.
When the glaze is ready, whisk in 2 tablespoons unsalted butter until melted, then remove from the heat. When the chicken is ready, transfer it to a plate. Carefully pour off all but 1 tablespoon of the fat in the pan. Return the chicken to the pan skin-side up, and spoon the glaze evenly over it.
Transfer the pan to the oven and bake for 5 minutes. Spoon some of the glaze in the pan back over the chicken, then continue baking until the chicken reaches an internal temperature of 165°F, 5 to 7 minutes more. Turn the oven on to broil, and broil until the skin is dark golden brown and the sauce is bubbling, 1 to 2 minutes.