Pat the chicken thighs dry and season both sides with 1/2 teaspoon salt, the pepper, and the dried thyme.
Heat the olive oil in a large skillet over medium-high heat. Sear the chicken 5-6 minutes per side until deeply golden and cooked through to 165°F; work in batches if the skillet looks crowded, then transfer to a plate.
Add the Brussels sprouts cut side down to the skillet and cook undisturbed for 4 minutes until nicely browned. Stir in the apple wedges and garlic and cook 2 minutes more.
Whisk the apple cider and Dijon mustard together, pour into the skillet, and scrape up the browned bits as it comes to a simmer.
Return the chicken and any juices to the skillet, reduce heat to medium-low, cover, and simmer 6-8 minutes until the sprouts are tender and the sauce has slightly thickened.
Taste and add the remaining 1/4 teaspoon salt if needed, spoon the pan sauce over everything, and scatter with fresh thyme if using.