In a large skillet, combine the apples, butter, cinnamon and sugar over low heat, and cook, stirring occasionally, for 1 to 1 1/2 hours.  The mixture will release a lot of water, the apples will break down and the mixture will be golden in color when done.  Some bits may darken and caramelize – this is a good thing.  Remove the skillet from the heat, stir in the vanilla, and either cool before using, or cool completely and refrigerate until you wish to make your turnovers.

To make the turnovers, line a baking sheet with parchment and preheat the oven to 350 – you need puff pastry rolled and cut into 5 1/2 to 6-inch squares.  Put about 1/4 cup of filling onto one side of the square, use a spoon to spread it around the half triangle evenly and leave some border to seal the turnover.  Brush all exposed pastry lightly with the egg, fold the square over to make a perfect triangle and then use a fork to pinch together the edges.  Transfer the turnover to your baking sheet and finish putting together as many turnovers as you’re planning to bake.  At this point, the turnovers can also be well-wrapped and frozen, just bake them directly from the freezer.

Use the tip of a sharp knife to make small slits at the top of each turnover, brush each completely with egg, liberally sprinkle with sugar and then bake for 20-30 minutes.  Watch them – if you’ve made your own dough or rolled the pastry yourself, they could take as long as an hour – with the perfectly evenly store-bought version that I used, 20-25 minutes worked.  Allow the turnovers to cool long enough to not scald your mouth when you bite into one – eating them at room temperature, randomly, in the middle of the day, is also highly recommended.