Preheat the oven to 350°F.

In a bowl, thoroughly whisk together the unsweetened applesauce, packed brown sugar, Dijon mustard, honey, and finely chopped rosemary until the mixture is evenly blended.

Blot the pork tenderloin thoroughly with paper towels to remove surface moisture, which helps create a well-browned exterior during searing.

Season the tenderloin evenly with the salt and freshly ground black pepper, covering the sides and ends as well as the main surface.

Pour the vegetable oil into a large oven-safe skillet and heat it over medium-high heat until the oil begins to shimmer.

Carefully add the seasoned pork tenderloin. Sear it without unnecessary movement for approximately 2–3 minutes per side, allowing a golden-brown crust to develop over the exterior.

Sear each end for about 1 additional minute so the tenderloin develops an evenly caramelized surface.

Pour the prepared applesauce mixture over the browned pork tenderloin, spreading the glaze so it coats the top and sides evenly.

Place the oven-safe skillet in the preheated oven and bake at 350°F for 30–40 minutes. Cook until a meat thermometer inserted into the thickest portion of the tenderloin registers 155°F.

Begin checking the internal temperature roughly 5 minutes before the expected cooking time is complete to help prevent the tenderloin from becoming overcooked.

As the pork bakes, the applesauce mixture will reduce and lightly caramelize, forming a glossy, deep-colored coating around the meat.

Remove the skillet from the oven and allow the pork tenderloin to rest for 10 minutes before cutting it. This resting period gives the juices time to redistribute throughout the meat.

Cut the tenderloin crosswise into slices approximately 1/2 inch thick. Spoon the caramelized applesauce glaze from the skillet over the sliced pork before serving.