Place oven rack in center position and preheat oven to 350°F.
Combine applesauce, honey, mustard, and rosemary in a small bowl and stir to combine. Season with salt and pepper, to taste. Set aside.
Heat oil in a large oven-safe skillet over medium heat. Generously season the pork roast with salt and black pepper, to taste. Cook until browned on all sides, about 5-10 minutes.
Remove from heat and spread half of the applesauce mixture on the top and sides of the pork. Arrange the chopped apples around the sides of the pork and place in the preheated oven.
Roast for 20 minutes, then remove from oven and turn the pork. Stir the apples, brush pork with remaining applesauce mixture and return to the oven until the pork is cooked through, about 20 more minutes.
Move tenderloin from pan to cutting board (or serving plate), tent with aluminum foil and let rest for 5 minutes before serving with the cooked apples.