Preheat oven to 375° F.
Drain and dice the apples. In a large skillet, heat 1 Tbsp of olive oil over medium heat and saute onions and apples until caramelized, about 10 minutes.
In the pan, add the thyme, sage, 1 tsp of salt and the apple sauce. Stir together a few minutes. Remove the chutney from the pan and set aside in a small bowl to cool completely.
Return the skillet to the stove and heat the remaining 1 Tbsp of olive oil over medium high heat. Season the pork with the remaining 1/2 tsp salt. Sear the pork 3 minutes on each side and then remove from the pan to cool.
Lay out the puff pastry on a clean dry surface. Place 1/2 the chutney in the center pastry and spread about the same size as the tenderloin. Top the chutney with the pork. Add the remaining chutney on top of the pork.
Pull the 4 sides of the puff pastry around the tenderloin and seal tightly. Place the "seam" side down on the tray. Brush the pastry with the egg white. Bake for 20-25 minutes or until the thermometer inserted into the pork reads 155° F. Slice and serve.