For the brine: In a large saucepan, combine the water, vanilla beans and seeds, cinnamon sticks, cloves, and black peppercorns. Bring to a boil over medium heat. Add the sugar and salt; stir to dissolve. Turn off the heat, and then cool to room temperature (this can take an hour or so; put it in the fridge to hasten the process. Alternatively, you can boil only 4 cups of water and then add 5 cups of ice cubes).

When cool, pour the brining solution into a container large enough for the pork and the solution, such as a disposable aluminum roasting pan. Cover and refrigerate overnight or up to 24 hours.

Preheat the oven to 325 degrees F.

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.

Add 2 tablespoons 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 1 cup cider, scraping up any brown bits. Stir in the brown sugar.

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 1 cup. Transfer the pan to the oven. Roast until a meat thermometer inserted in the center of the loin reads 145 degrees F, 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).

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.

Slice the pork into 1/2-inch thick slices. Arrange on the platter with the apples and celeriac. Drizzle the sauce over the meat.