-
Fill a large pot with 2 quarts water; add 1 1/2 cups salt and sugar. Bring to a boil over high heat and cook until salt and sugar are dissolved. Remove from heat and let brine cool completely.
-
Place pork in a large container and cover with brine. Transfer to refrigerator and let marinate for 45 minutes. Remove pork from brine and pat dry with paper towels.
-
Preheat oven to 425 degrees with rack in the center. Fit a roasting pan with a rack and set aside.
-
Season pork with remaining 1 teaspoon salt and 3/4 teaspoon freshly ground pepper. Place pork on rack and transfer to oven; cook until an instant-read thermometer reaches 130 degrees when inserted into the thickest part of the pork, about 45 minutes.
-
Meanwhile, place cider in a medium saucepan over medium-high heat until reduced and turns into a dark golden-brown loose syrup, about 20 minutes. Remove from heat and add vinegar; stir to combine. Pour glaze into a small bowl and transfer to refrigerator; let cool.
-
In a small bowl, mix together paprika, cumin, remaining 1/2 teaspoon black pepper, and chile powder; set spice mixture aside.
-
Brush half of the glaze over pork and return to oven for 2 minutes more. Remove from oven and let stand for 15 minutes; brush with remaining glaze and sprinkle with spice mixture.
-
Cut the pork rack into chops by cutting between each set of bones; transfer chops to a large platter. If any glaze remains, add juices from pork to glaze and stir to combine; pour over chops and serve immediately.