Heat 2 teaspoons of oil in a large skillet over medium-high. Sprinkle the top of the chicken evenly with 1/2 teaspoon kosher salt and 1/4 teaspoon pepper. Once the oil is hot and shimmering, add the chicken to pan, top-side down. Let cook 4 minutes, then flip and continue cooking until the meat is cooked through and reaches an internal temperature of 165 degrees F. Remove to a plate and cover with foil to keep warm.

In a small bowl or large measuring cup, stir together the apple cider and mustard. With a paper towel, carefully wipe the skillet clean. Add the remaining 2 teaspoons of oil to the pan over medium high. Once the oil is hot, add the apple slices, remaining 1/2 teaspoon salt, 1/4 teaspoon pepper, and rosemary. Cook 5 minutes, until the apples are lightly tender and begin to turn golden. Return the chicken to pan and pour the cider mixture over the top. Let cook for 4-5 minutes, until the liquid is reduced by half. Serve warm, sprinkled with additional chopped rosemary as desired.