Preheat the oven to 400 degrees F and use butter to grease a 9x13-inch baking dish.
On a floured surface, roll pie dough into a large rectangle. Slice dough into six squares. Place an apple in the center of each square with the hollowed core facing upwards.
Cut butter into 8 long, skinny pats and insert 1 pat in the core of each apple. Remaining butter will be used in sauce.
Sprinkle brown sugar, cinnamon, and nutmeg over apples and into core.
Wet your fingers, then bring each corner of the dough up to the center. Pinch the dough along the seams to seal. Repeat with the remaining apples, then transfer to the prepared baking dish.
For the sauce: add water, remaining brown sugar, vanilla extract, and remaining butter to a large saucepan. Bring mixture to a boil over medium heat, then reduce the heat to low and simmer until sugar is dissolved, about 3-4 minutes.
Carefully pour sauce over the dumplings in baking dish.
Bake for 50-60 minutes or until golden in color.
Serve warm. Spoon sauce over individual dumplings when serving.
