Prepare the chicken thighs by seasoning with salt and pepper.
In a large skillet, heat olive oil over medium-high heat. Add the seasoned chicken thighs skin-side down and sear until golden brown, about 5-7 minutes.
Flip the chicken and sear the other side for an additional 5 minutes.
Reduce heat to medium and add the apple cider, Dijon mustard, and apple cider vinegar to the skillet, stirring to combine.
Cover the skillet and let the chicken simmer in the sauce for about 25-30 minutes, or until the chicken reaches an internal temperature of 165°F.
Remove the lid, increase the heat to high, and let the sauce reduce for another 5-7 minutes until sticky.
While the chicken is finishing, prepare the slaw by combining shredded cabbage, carrots, cranberries, apple cider vinegar, honey, salt, and pepper in a large bowl.
Serve the sticky apple cider chicken over a bed of crisp autumn slaw, drizzling any extra sauce over the top.