Season the chicken. If possible, take the chicken thighs out of the refrigerator about 20–25 minutes before cooking. Mix the coriander, dried rosemary, dried thyme, cinnamon, nutmeg, salt, and black pepper in a small bowl. Rub the seasoning mixture evenly over all sides of the chicken.
Heat the skillet. Add the olive oil and half of the butter to a large skillet over medium-high heat. Allow the butter to melt and the skillet to become hot.
Sear the chicken. Place the seasoned chicken thighs into the skillet. Cook without moving them for 4–5 minutes, or until the bottoms are deeply golden brown. Flip and continue cooking for another 4–5 minutes, or until the chicken reaches an internal temperature of 165°F. If needed, partially cover the skillet to help the chicken cook through. Transfer the chicken to a plate.
Prepare the apples and onion. While the chicken cooks, slice the red onion and core and thinly slice the apples. Leave the apple skins on for extra color and texture.
Deglaze the skillet. Add a small splash of apple cider to the hot skillet and scrape up the browned bits from the bottom with a wooden spoon.
Build the sauce. Add the remaining butter and Dijon mustard, followed by the sliced red onion. Cook for 1–2 minutes, stirring occasionally.
Add the apples. Stir the sliced apples into the skillet and cook briefly until they begin to soften.
Simmer. Pour in the remaining apple cider. Simmer for 3–4 minutes, allowing the liquid to reduce slightly and form a light, flavorful sauce.
Finish the dish. Taste the sauce and adjust the salt and black pepper as needed. Reduce the heat to medium-low and return the chicken thighs to the skillet. Warm for 1–2 minutes, spooning the apple cider sauce over the chicken.
Serve. Garnish with fresh thyme and rosemary if desired, and serve the Apple Cider Chicken Skillet immediately.