Make the dough: In a large bowl, whisk together the flour, baking powder, and salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs. Gradually add the cold milk, mixing until just combined. Do not overmix.
Chill the dough: Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.
Prepare the apples: While the dough is chilling, prepare the apples. Peel, core, and cut the apples into wedges. In a bowl, combine the granulated sugar, cinnamon, and nutmeg. Toss the apple wedges in the sugar mixture.
Roll and fill: On a lightly floured surface, roll out the chilled dough to about ¼ inch thickness. Cut the dough into squares (about 4-5 inches).
Assemble the dumplings: Place a few apple wedges in the center of each dough square. Top with a few small pieces of butter. Bring the corners of the dough square together and pinch to seal, forming a dumpling.
Make the syrup: In a large skillet or Dutch oven, combine the water, granulated sugar, cinnamon, and nutmeg. Bring to a boil over medium heat, stirring until the sugar is dissolved. Add the butter and cook until melted.
Fry the dumplings: Carefully place the dumplings in the simmering syrup, leaving some space between them. You may need to do this in batches depending on the size of your skillet. Cook for about 20-25 minutes, or until the dumplings are golden brown and cooked through. You may need to turn them gently during cooking to ensure even browning.
Serve: Remove the dumplings from the skillet and serve warm, drizzled with the remaining syrup.