In a large bowl, mix 4 cups cider, 2 cups cold water, 4 tbsp. salt, bay leaves, garlic cloves, and chile flakes. Add pork chops, cover bowl, and chill, turning meat occasionally, at least 3 hours and up to 1 day.
Preheat oven to 325º. Remove pork chops from the brine and blot dry. Melt 2 tbsp. butter in a large frying pan over medium-high heat. Add pork chops (you may need to do this in 2 batches) and cook for 3 to 5 minutes, or until well browned. Flip chops and cook another 3 to 4 minutes, until browned on that side. Layer chops in a 9- by 13-in. baking pan and bake until barely pink in the center (cut to test), 15 to 20 minutes.
Meanwhile, pour remaining 3/4 cup cider into the hot frying pan, scraping pan with a wooden spoon to dislodge browned bits. Add the chicken stock, turn the heat to high, and boil until liquid is reduced to about 1/2 cup, 8 to 10 minutes. Remove from heat and stir in remaining 1 tbsp. butter and the mustard. When sauce is no longer bubbling, stir in crème fraîche. Season with remaining 1/2 tsp. salt and the pepper. Remove the pork from oven and spoon a generous amount of sauce over each chop. Serve topped with sautéed apples.
Note: Nutritional analysis is per serving; sodium data not available.