In a medium saucepan over medium heat, combine the apple cider, granulated sugar, and 2 tablespoons of unsalted butter. Bring the mixture to a boil. Then, reduce the heat and let it simmer for about 5 minutes, stirring occasionally.

After simmering, remove from heat. Stir in the vanilla extract. Set aside.

Preheat oven to 400°F (200°C). Spray a 9x13-inch baking dish with nonstick cooking spray and set it aside.

On a lightly floured surface, roll out pie dough into a large rectangle, approximately 24x16 inches and about 0.25-inch thick. Cut the dough into six even squares, about 8x8 inches each.

Place a peeled and cored apple in the center of each dough square.

Fill the hollow core of each apple with 1 tablespoon of softened butter.

In a small bowl, mix together the light brown sugar, ground cinnamon, and ground nutmeg. Evenly sprinkle this mixture over the apples.

Lightly moisten the edges of each dough square with water. Then, carefully fold the dough around the apples, pinching the edges to seal them completely.

Place the wrapped apples into the prepared baking dish.

Pour the prepared sauce over the dumplings in the baking dish.

Cover the dish with aluminum foil and bake for 25 minutes.

After 25 minutes, remove the foil and bake for an additional 25-30 minutes, or until the dumplings are golden brown and crisp on top.

Serve the dumplings warm with vanilla ice cream and extra sauce from the baking dish.