Preheat the oven to 350 degrees. Coat the pork with the oil; season with salt and pepper. In a large, nonstick ovenproof skillet, cook the pork over moderately high heat until browned all over, 3 minutes per side. Transfer the skillet to the oven and roast for about 18 minutes, turning twice, until an instant-read thermometer inserted in the thickest part of the meat registers 140 degrees.

Transfer the pork to a carving board and let rest for 10 minutes. Add the apple juice, broth, soy sauce, raisins, and ginger to the same skillet and bring to a boil. Cook until the liquid has reduced by half, 4 minutes. Stir in the cornstarch slurry and cook, stirring, until thick enough to coat a spoon, about 30 seconds; remove from the heat.

Carve the pork and arrange on plates. Stir any carving juices into the pan sauce. Spoon the sauce over the pork and serve.