Place oven rack in center position and pre-heat oven to 350°F.
Combine applesauce, honey, Dijon mustard, and rosemary leaves in a small bowl and stir to combine. Season with salt and black pepper, to taste, and set aside.
Heat coconut 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 and evenly seared on all sides, approximately 5-10 minutes.
Remove from heat and spread half of the applesauce mixture all over the top and sides of the pork. Arrange the chopped apples around the sides of the pork and place in the pre-heated oven.
Roast for 20 minutes, then remove from oven and flip the pork. Brush with remaining applesauce mixture and return to the oven for another 20-25 minutes, or until the pork is cooked through.
Remove from oven and cover loosely to rest for 5 minutes before serving.