Creating Old-Fashioned Apple Dumplings is both enjoyable and rewarding when you follow these simple steps:

1. Preheat Oven: Preheat your oven to 375°F (190°C).
2. Prepare Apples: Peel and core the apples, making a hole in the center. Set aside.
3. Make Dough: In a large bowl, mix the flour, salt, and baking powder. Cut in the butter until the mixture resembles coarse crumbs.
4. Form Dough: Gradually add water and mix until a soft dough forms. Cover it and let it rest for about 10 minutes.
5. Roll Out Dough: On a floured surface, roll out the dough into a large rectangle, about 1/8 inch thick.
6. Cut Squares: Cut the dough into 6 equally sized squares, large enough to wrap around the apples.
7. Stuff Apples: In a small bowl, mix granulated sugar, brown sugar, cinnamon, and nutmeg. Sprinkle the mixture into the center of each apple.
8. Assemble Dumplings: Place each apple at the center of a square of dough. Fold the corners over the apple and pinch to seal.
9. Prepare Baking Dish: In a medium bowl, combine water, vanilla extract, and lemon juice. Pour half of this mixture into a greased baking dish.
10. Arrange Dumplings: Place the dumplings in the baking dish, seam-side down. Pour the rest of the liquid over the dumplings.
11. Brush with Egg: Brush the tops of the dumplings with the beaten egg for a golden finish.
12. Bake: Bake in the preheated oven for 45-50 minutes or until the dough is golden and the apples are tender.
13. Cool: Remove from the oven and let cool for 10-15 minutes before serving.

The step-by-step process is straightforward, ensuring you’ll have success every time you make these delightful dumplings.