In a small saucepan, combine the water, white sugar, vanilla, 1 tablespoon butter, and the nutmeg over high heat. Bring to a boil for 1 minute; set aside.
In a small bowlk combine the brown sugar cinnamon, and remaining 1 tablespoon butter; mix well.
Unroll pastry and cut into quarters. Stuff each apple cavity with an equal amount of brown sugar mixture and place on a pastry quarter. Fold pastry up around apples and pinch ends together to completely enclose apples. Place dumplings seam-side down in an 8-inch square baking dish and pour sugar sauce over the top.
Bake 45 to 50 minutes or until golden. Serve warm, drizzled with sugar glaze from bottom of baking dish.
Notes: Small apples work great for this recipe but they're not always available, so go ahead and use the regular-sized ones cut in half.