Look for a mild pecorino from Tuscany, sometimes called caciotta.
Preheat the oven to 350 degrees. Halve and peel the pears, and carefully remove the seeds and core.
Melt the butter in a large cast-iron skillet over medium heat. Arrange the pears, cut side down, in the skillet so they just touch one another. Sprinkle the sugar, over the pears and butter. Cook, tilting the pan back and forth gently from time to time, until the sugar dissolves and melts into a golden caramel, about 4 minutes. Scrape the vanilla seeds into the pan, and add the pod. Reduce the heat, add the brandy, and cook a few minutes more. Be aware that the brandy may ignite, but the flames will die down quickly.
Carefully turn the pears over, and transfer to the oven. They should be deep golden brown. Roast until the pears are fork tender, about 10 minutes, depending on the ripeness and size of the pears. Serve with thick slices of pecorino and caramel sauce.