Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper for easy cleanup.
Peel, core, and thinly slice the apples. In a medium bowl, combine the sliced apples with the brown sugar and a few dashes of cinnamon. Set the apple mixture aside.
In another bowl, cream together the softened cream cheese and vanilla extract until smooth. Beat in the egg until well combined. Set the cream cheese mixture aside.
Place the pastry puff shells on the prepared baking sheet, and bake for 15 minutes, or until the pastry is golden brown and mostly risen.
Remove the shells from the oven. Use a knife to remove the "tops" or the inside of the shells to fill.
Fill each tart shell 1/3rd of the way with the cream cheese mixture. Then, top with apple slices.
Bake in the oven for another 10 minutes at 375°F, until the edges are brown and filling is bubbly.