Season & Sear Chicken: Pat chicken thighs completely dry with paper towels. Season generously all over with kosher salt and black pepper. Heat olive oil and 1 tbsp butter in a large deep cast-iron skillet over medium-high heat. Place chicken thighs skin-side down and sear undisturbed for 7 to 8 minutes until skin is deeply golden, shatteringly crisp, and rendered. Flip and sear for 3 minutes on the flesh side. Transfer chicken to a plate.

Caramelize Apples & Aromatics: Pour off all but 1 tablespoon of fat from the skillet. Add remaining 1 tbsp butter, sliced apples, and shallots. Sauté over medium heat for 4 to 5 minutes until apple edges soften and caramelize lightly. Stir in minced garlic and cook for 30 seconds until fragrant.

Build the Cider Glaze: Pour in unfiltered apple cider and chicken broth, scraping up all browned bits from the pan bottom. Whisk in Dijon mustard and maple syrup. Bring liquid to a vigorous simmer and let reduce by half for 3 to 4 minutes into a glossy, fragrant sauce.

Braise & Thicken: Nest skin-seared chicken thighs back into the skillet between apple wedges (keeping the crispy skins above the liquid so they stay crisp). Scatter rosemary and thyme sprigs into the sauce. Lower heat to medium-low, cover loosely, and simmer for 12 to 14 minutes until chicken reaches an internal temperature of 175°F.

Spoon Glaze & Serve: Uncover pan and spoon bubbling glossy cider reduction over the apples and chicken base. Rest 5 minutes, then serve hot over velvety mashed potatoes or buttered egg noodles.