Slice the pears in half and core them. Cut the halves into fairly even sized slices.
Heat a 10" cast iron skillet over medium heat with the butter. Once the butter has melted add the brown sugar, cinnamon, and star anise.
Allow the butter and sugar to cook until the sugar has dissolved, and it has started to slightly thicken.
Add the red wine and continue to cook until the sauce has reduced. It should coat the back of a spoon and hold its shape when you run your finger down the middle.
Arrange the pears on top of the caramel sauce.
Roll the puff pastry over the top of the cast iron skillet. Tuck in the edges.
Cut a small slit in the center of the puff pastry so the steam can escape.
Bake the tarte tatin for 35-40 minutes, or until the puff pastry is golden brown.
Allow the tarte to cool for 10 minutes.
Place a large plate over the top of the skillet, and flip it, inverting the tarte tatin onto the plate, pear side up.