Start making your pear puff pastry tarts by preheating your oven to 200°C (375°F).
Using a small bowl, combine the brown sugar, cinnamon powder, ground cardamom, nutmeg, and salt. Set aside.
Unroll the puff pastry on a flat surface and cut it into 9 (almost equal) portions.
Place them on top of a tray lined with a baking sheet, then brush each portion with the beaten egg.
Sprinkle some off the spices and sugar mixture, avoiding the sides of the pastry.
Arrange a halved, sliced pear in the middle of the pastry.
Sprinkle more of the sugar and spices mixture on top of the pear.
Dot each pear with two bits of butter.
Place the tray of pear puff pastry tarts in the middle of the oven for 18 to 20 minutes, or until the top has turned golden.
Sprinkle some powdered sugar on your pear tart, if desired.
Serve.