Preheat the oven to 400˚F.
Peel the pears, then halve them and scoop out the seeds. Cut each half into halves or thirds and set aside.
Heat a heavy-duty pan (like our @AllClad copper core pan) over medium heat. Once hot, evenly spread the sugar in the pan. Watch as the sugar slowly melts and turns brown. When the edges caramelize, gently stir the melted sugar to the center of the pan. Lumps may form, but keep stirring. Eventually, the sugar should become smooth and medium-dark amber.
Remove from heat, add butter, and whisk until it combines. Return to medium heat and add the pear slices. The caramel may seize up, but don’t worry—when the pears release moisture, the caramel will soften into a smooth sauce. Stir in vanilla, cinnamon, and nutmeg.
Cook for about 10 minutes until the pears are fork-tender. Using a spoon, transfer ¾ of the caramel to a smaller 10-inch pan. Simmer for a few minutes until thickened. Remove from heat, then arrange the pears rounded side down on top of the caramel. Pour any remaining caramel over the pears.
Tuck the puff pastry round down the sides of the pan. Bake for 30 minutes, then let it cool for 30-45 minutes before flipping it upside down and serving.