Heat the olive oil in a skillet over medium-high heat. Season the pork tenderloin halves with salt and pepper to taste, then cook in the hot oil until evenly browned on all sides, about 8 minutes. Reduce the heat to medium-low, and cook until the pork is no longer pink in the center, turning occasionally, about 25 minutes. An instant-read thermometer inserted into the center should read 145 degrees F (63 degrees C). Place the pork onto a plate, cover with two layers of aluminum foil, and allow to rest in a warm area for 10 minutes.
While the pork is resting, pour the wine into the pan; bring to a simmer while scraping the browned bits of food off of the bottom of the pan with a wooden spoon. Simmer for 2 minutes, then add the apples, chicken stock, vinegar, cinnamon, nutmeg, brown sugar, and nutmeg. Cook and stir until the apples are tender, about 10 minutes. Stir cornstarch mixture into the simmering sauce to thicken. Cook and stir 1 minute more until the sauce thickens and is no longer cloudy.
Slice the pork tenderloin into 1/4 inch thick slices, and arrange on a serving platter. Pour the apple sauce over meat to serve.