Whisk together the egg and water to make your egg wash. Set aside.
Add a sheet of parchment paper to your work surface and add a dusting of flour. Carefully unfold a sheet of puff pastry onto the board. Dust your rolling pin with flour, and begin to roll out the dough to a 16” x 12” rectangle. You may need to rotate the dough to make sure it's even. Slide the pastry and the parchment onto a baking sheet. Using a pairing knife, slice a 1” border around all sides so that you have 4 long strips. Brush the borders of the dough rectangle with a bit of egg wash,and carefully place the strips of dough back on top of the dough, like you’re making a picture frame.
To the dough, add ⅔ cup the pecan filling and spread out in an even layer in the center of the “frame”. Carefully arrange the sliced apples on top of the pecan filling in rows, overlapping them tightly.Atop the apples, using a pastry brush, glaze the apples with ⅓ of the glaze. (You’ll use the rest basting the tart halfway through and for drizzling.)
To finish, brush the sides of the tart with the egg wash and sprinkle the sides of the dough with a bit of turbinado sugar (if using).
Transfer to the oven on the middle rack and bake for 20 minutes. At the 20 minute mark, brush the apples with another ⅓ of the glaze and transfer back to the oven. Reduce the heat down to 350, and cook for an additional 10 minutes until the crust is puffed, apples are cooked, and the glaze is caramelized.
To serve, brush with the remaining glaze and serve warm with vanilla ice cream, if desired.