Pat the chicken thighs dry with a paper towel. This is crucial for getting the skin crispy. Season both sides of the chicken generously with salt and black pepper.
Heat the olive oil in a large oven-safe skillet over medium-high heat. Place the chicken thighs in the pan, skin-side down. Cook for 6 to 8 minutes without moving them until the skin is golden brown and crispy. Flip the chicken and cook for another 2 to 3 minutes, then remove the chicken from the pan and set it aside on a plate.
Drain all but one tablespoon of the chicken fat from the skillet. Add the minced garlic and cook for about 30 seconds until fragrant, being careful not to let it burn.
Pour the apple cider, apple cider vinegar, honey, Dijon mustard, and thyme into the skillet. Use a wooden spoon to scrape up any browned bits from the bottom of the pan, as these hold a lot of flavor.
Bring the liquid to a simmer over medium heat. Place the chicken thighs back into the skillet, skin-side up. Let the mixture simmer for about 12 to 15 minutes, or until the chicken is cooked through (reaching an internal temperature of 165°F) and the sauce has reduced by half to a thick, syrupy consistency.
Remove the skillet from the heat. Stir in the tablespoon of butter to give the glaze a glossy finish. Spoon the thickened cider glaze over the top of the chicken thighs before serving.