Pat the chicken thighs dry with paper towels and season both sides with salt and black pepper.
Heat the olive oil in a large Dutch oven or deep skillet over medium-high heat.
Place the chicken skin-side down and sear for 5 to 6 minutes until golden brown. Flip and cook for another 2 minutes, then transfer to a plate.
Reduce the heat to medium and melt the butter.
Add the sliced onion and cook for 5 minutes until softened.
Stir in the garlic and cook for 30 seconds until fragrant.
Add the apple slices and cook for 2 minutes.
Pour in the apple cider and chicken broth, then stir in the Dijon mustard, brown sugar, thyme, and rosemary.
Bring the mixture to a gentle simmer.
Return the chicken thighs to the pan, skin-side up.
Cover and cook over low heat for 35 to 40 minutes, until the chicken is tender and reaches an internal temperature of 165°F (74°C).
Remove the lid and simmer for another 5 to 10 minutes to slightly reduce the sauce.
Serve the chicken with the apples, onions, and plenty of the apple cider sauce.