Make the vegan "buttermilk:" Place the full-fat coconut milk and the apple cider vinegar into a small glass bowl and set aside.
Sprinkle chicken with salt and pepper, then place chicken in 1 gallon freezer-safe bag or container, then pour "buttermilk" over top, make sure chicken is coated, then seal and place in refrigerator to marinate for at least 4 hours.
2.5 hours ahead of when you plan to serve the dish, preheat the oven to 350 degrees and remove the marinated chicken from the refrigerator.
Add olive oil to the bottom of a large, unheated skillet and swirl so the bottom of the skillet is coated.
Remove the chicken thighs from the "buttermilk" marinade, then carefully place in the skillet, skin side up in a single layer, then discard the marinade.
In a small bowl, combine the mustard and wine, then spoon the mustard sauce on top of the chicken breasts and spread it around to coat the tops of the chicken thighs.
Sprinkle the tops of the chicken thighs with fresh thyme, smoked paprika, and more salt and pepper.
Place the skillet in the preheated oven and roast for 30 minutes.
Remove the skillet from the oven, then use tongs to transfer the chicken to a plate to rest.
Carefully place the sliced potatoes, minced garlic, and some salt and pepper to the skillet. Toss to coat with the pan juices, then spread out the potatoes into an even layer.
Place the chicken thighs back on top of the potatoes, then place skillet back in the oven to roast for another 30 minutes, or until a meat thermometer reads 155 degrees F.
Remove chicken thighs to a clean plate, then return the skillet with the potatoes to the oven, increase the oven temperature to 425 degrees F and roast for about another 15 minutes or until the potatoes are tender and slightly brown.
Remove the skillet from the oven, place chicken thighs on top, garnish with parsley and chives and serve hot from the pan.
