Marinate the Chicken: In a bowl or resealable bag, combine apple cider, olive oil, apple cider vinegar, garlic, rosemary, Dijon mustard, salt, and pepper. Add the chicken and marinate for at least 30 minutes, or up to 4 hours in the refrigerator.

Sear the Chicken (if using boneless, skinless breasts): Heat a large skillet over medium-high heat. Remove chicken from the marinade (reserve the marinade!). Sear the chicken for 3-4 minutes per side, until golden brown. Remove chicken from skillet and set aside. For bone-in, skin-on thighs, start skin-side down and sear until crispy and golden brown, about 6-8 minutes. Flip and sear for another 3-4 minutes. Remove from skillet.

Sauté the Apples: Add the sliced apples to the skillet and cook for 2-3 minutes, until slightly softened and caramelized. If using, add the butter now for enhanced flavor.

Create the Sauce: Pour the reserved marinade into the skillet and bring to a simmer. Cook for 5-7 minutes, until the sauce has slightly thickened.

Return Chicken to Skillet: Place the chicken back into the skillet with the sauce and apples. If using boneless breasts, ensure they are submerged about halfway in the sauce. For bone-in thighs, nestle them amongst the apples.

Simmer and Cook: Reduce heat to medium-low, cover the skillet, and simmer for 15-20 minutes for boneless breasts, or 25-30 minutes for bone-in thighs, or until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).

Serve: Garnish with fresh rosemary sprigs, if desired. Serve hot with your favorite side dishes.