Cut peaches in half and remove the pits. Combine orange juice, sugar, brandy and vanilla. Add peaches to mixture and let marinate for a couple of hours (or overnight).
Roll pastry out to 1/4" thickness and cut into 3" rounds. Dock pastry with a fork and brush both sides with butter.
Clean and oil grill. Grill rounds of pastry over moderate heat. Flip when first side is golden brown and has formed a nice crust. Don't worry if the edges burn a little, that's all part of the flavor. Set aside.
Remove peaches from the marinade and set aside. Pour the marinade into a small pot and bring to a boil. Reduce heat and simmer until thick and syrupy.
Meanwhile, grill peaches, cut side down, until caramelized and soft. Arrange each half on a round of pastry and drizzle with sauce.