Season the chicken: Pat chicken thighs dry. Season both sides with salt and pepper. Dry skin helps with a crisp sear.
Sear the chicken: Heat olive oil in a large skillet over medium-high heat.
Add chicken skin-side down and cook 5–7 minutes until deeply golden; flip and cook 3–4 minutes. Transfer to a plate. Leave drippings in the pan.
Sauté the aromatics: Reduce heat to medium.
Add butter, then onions. Cook 4–5 minutes, stirring, until they soften and start to brown.
Add apples and garlic: Stir in apple slices and cook 3–4 minutes until slightly tender with light color. Add garlic and thyme; cook 30 seconds until fragrant.
Deglaze with cider: Pour in apple cider and chicken broth.
Scrape up browned bits from the bottom of the skillet; they add big flavor.
Build the sauce: Whisk in Dijon. Nestle chicken back into the pan, skin-side up. The liquid should come about halfway up the chicken.
Simmer to finish: Reduce heat to medium-low.
Cover and cook 12–15 minutes, or until chicken reaches an internal temperature of 165°F.
Optional thickening: Remove chicken to a plate. If you want a thicker sauce, stir in the cornstarch slurry and simmer 2–3 minutes until glossy. Add a splash of apple cider vinegar to brighten, if desired.
Taste and adjust salt and pepper.
Serve: Return chicken to the skillet or plate with apples and onions. Spoon sauce over the top. Garnish with parsley.
Serve hot with mashed potatoes, rice, polenta, or crusty bread.