Preheat oven to 400 degrees F. Grease a 10-inch cast iron pan with butter.
Pour red wine into a large pot and add sugar, honey, cinnamon stick, cloves, and star anise. Squeeze juice from ½ orange and add to the pot. Slice the other orange half and add to the pot. Bring to a boil over medium heat and add the pears. Scrunch up a sheet of parchment paper and place directly on top of the pears to keep them submerged. Reduce heat to low and continue to simmer for 20 minutes, rotating the pears halfway through.
Remove pears with a slotted spoon and place in a colander to drain excess liquid. Remove orange slices and spices from wine. Increase heat to medium and continue to simmer until reduced to ½ cup and the liquid is thick and syrup. Keep an eye on the wine because once it starts to reduce, it can easily burn. Remove from heat and set aside.
In a large saute pan, add ¾ cup sugar in an even layer. Heat the pan over medium heat and melt the sugar, continuing to cook until it turns amber brown in color. Remove from heat and stir in the butter, whisking until well combined. Add 2 tablespoons reserved reduced mulled wine, stirring to combine. Return the pan to medium heat and add the pears, gently stirring the pears to coat in the caramel. Continue to simmer for 10 minutes.
Remove pears and transfer to prepare cast iron pan, arranging the pears with the cut side facing up. Drizzle ¼ cup of the caramel sauce on top, reserving the remaining sauce for serving. Let rest for 10 minutes.
Meanwhile, lightly dust a work counter with flour and roll out the puff pastry so that it's 2-inches bigger than the cast iron pan. Place puff pastry on top of the pears, tucking in the edges. Use a sharp knife to cut 3 slits in the puff pastry.
Bake the mulled wine pear tarte tatin for 30-35 minutes or until the pastry is golden brown. Remove from oven and let cool for 30 minutes.
Place a plate directly on top of the tart and with one hand firmly securing the plate, carefully tip skillet over a bowl to drain any juices. When all the juices have been transferred to a bowl, carefully invert the pastry. If any pears shifted, rearrange them on the tart. Serve tarte tatin with vanilla ice cream and extra reserved mulled wine caramel if desired.