Preheat the oven to 375°F (190°C).
In a bowl, combine flour and salt for the pastry. Cut in the chilled butter until the mixture resembles coarse crumbs.
Gradually add cold water, stirring with a fork until the dough comes together. Form into a ball and chill if necessary.
On a floured surface, roll the dough out and cut into squares large enough to wrap around the apples.
Place each peeled and cored apple in the center of a dough square, then wrap and seal the edges.
Position the wrapped apples in a baking dish.
In a saucepan, mix sugar, water, butter, cinnamon, and nutmeg. Bring to a boil, then pour over the dumplings in the dish.
Bake for 45 minutes, basting occasionally with the syrup, until the apples are tender and pastry is golden brown.