Combine apple cider, honey, Dijon mustard, and minced garlic in a small saucepan. Simmer over medium heat, stirring occasionally, until thickened into a sticky glaze.
Heat cooking oil in a skillet over medium-high heat. Season chicken thighs with salt and pepper, then sear skin side down until golden and crisp, about 5-7 minutes.
Flip chicken and cook an additional 5 minutes until almost cooked through.
Pour the glaze over the chicken, reduce heat to medium-low, and cook gently while spooning glaze frequently until caramelized and sticky.
In a large bowl, combine shredded cabbage, carrots, and sliced apple. Whisk apple cider vinegar, celery seeds, salt, and pepper, then drizzle over slaw. Toss gently.
Stir chopped parsley or chives into the slaw for brightness.
Serve chicken thighs with a generous portion of crisp autumn slaw immediately.