In a mixing bowl, combine flour, baking powder, and salt. Cut in shortening until mixture resembles coarse crumbs. Stir in milk just until moistened.
Roll dough into a rectangle on a lightly floured surface. Cut into 4 squares. Place an apple on each square and fold dough over the apple, pinching edges to seal.
Place dumplings in a baking dish.
In a saucepan, combine sugar, water, butter, cinnamon, and nutmeg. Bring to a boil, then reduce heat and simmer for 5 minutes. Pour sauce over dumplings.
Bake for 35-45 minutes, until apples are tender and dough is golden brown.