Preheat the oven to 400˚F. Line a few baking sheets with parchment paper. Set them aside.
Add the caramelized apples, pork , sage, thyme, salt and pepper to a large bowl. Combine the ingredients until everything is well incorporated.
Lightly dust a clean work surface with flour. Roll out each sheet of puff pastry into a 8x12 inch rectangle. Cut each sheet in half lengthwise. Take one piece of dough and position it so that the longer sides are at the top and bottom. Portion a quarter of the sausage mix and form it into a log shape, about a half an inch away from the bottom edge of the puff pastry sheet. Mold it to the same length as the puff pastry.
Starting from the bottom edge, roll the dough up so that the bottom edge overlaps the top edge of the puff pastry. Roll the log back and forth where the edges meet to close the seam. Use a knife to cut the roll into 8 even pieces and place them onto the prepared baking sheet. Repeat this process with the remaining sausage mix and puff pastry.
Brush the tops of the sausage rolls with the egg wash. Sprinkle the everything seasoning on top. Bake the sausage rolls in the oven for about 30-33 minutes until the sausage is fully cooked and the puff pastry is golden brown. Remove them from the oven.