2) When cool, pour the brining solution into a container large enough for the pork and the solution, such as a disposable aluminium roasting pan. Cover and refrigerate overnight or up to 24 hours.
3) For the pork, preheat the oven to 160C/Gas 3.
4) Pull the pork out of the brine and pat dry with paper towels. Warm the oil in a large, ovenproof skillet over medium-high heat until nearly smoking. Add the pork to the pan and brown on all sides, about 15 minutes. Remove to a plate.
5) Add 2 tablespoons of butter to the pan and reduce the heat to medium. Add the apples and celeriac. Season with salt and saute until golden brown. Deglaze with vinegar and 230ml cider, scraping up any brown bits. Stir in the brown sugar.
6) Nestle the pork loin in the apples and celeriac and pour enough cider into the pan to keep things from burning on the bottom of the pan, about 225ml. Transfer the pan to the oven. Roast until a meat thermometer inserted in the centre of the loin reads 60C, about 45 minutes. Transfer the pork to a cutting board and let rest 10 minutes before carving (pork will continue to cook as it rests).
7) Meanwhile, return the pan to the stove over medium heat. Finish the sauce by adding in more cider if the pan is too dry. Stir in the remaining butter and the vanilla and black pepper. Taste for seasoning and readjust, if necessary.
8. Slice the pork into 1cm-thick slices. Arrange on the platter with the apples and celeriac. Drizzle the sauce over the meat.