Roll out thawed puff pastry and cut slightly larger than the 9" cake pan. Rest dough in fridge.
Fold parchment into a square, fold again, place tip in the center of pan, crease the edge, and trim. Lightly spray and line with the round parchment.
Peel, quarter and core apples, choosing similar sizes so they stack evenly.
Combine water, sugar, butter, salt, and vanilla in a large pot on medium heat until butter melts. Bring to boil, add half the apples and bring back to boil. Cover and reduce heat to low. Gently poach until a knife slides through easily (about 20-25 minutes). Remove with a slotted spoon and repeat with remaining apples.
In a small saucepan, melt ⅓ of the sugar over medium heat. Once dissolved, add the next ⅓ and mix. Add the remaining sugar and mix to combine until all dissolved. Stir until you achieve a deep amber color. Immediately pour into pan and swirl to coat the base.
Preheat oven to 400°F. Arrange the poached apples tightly in the pan and press down. Cover with the chilled puff pastry, fold edges backward, and brush with egg wash. Place on an oven tray and bake on lower rack for ~50 minutes or until golden brown.
Remove from oven and rest for about 10 minutes. Run a knife around the edge and invert a serving plate over the pan. Wrap a large kitchen towel over the dish and pan, hold firmly and
flip.
