Core the apples, leaving the base intact. If necessary, cut a thin slice from the bottom of each apple so it will stand upright.

In a food processor, pulse the walnuts until chopped. Add the butter, brown sugar, vanilla, ginger, cinnamon, and salt and process until blended. Stuff equal amounts of the nut mixture into the center of each apple. Place the apples on a plate, cover, and refrigerate until the butter mixture is firm, about 30 minutes.

Preheat the oven to 375°F. Line a rimmed baking sheet with parchment paper.

On a floured board, roll out 1 piece of dough into a 6” round disk, about 1⁄8” thick. Place an apple in the center and pull the dough up around the apple, creating a seal at the top by pleating and pinching the dough together. Repeat with the remaining dough and apples. Brush with the beaten egg and arrange on the prepared pan. Sprinkle with raw sugar. Bake until the apple is tender and the pastry is browned (the dumplings may leak slightly), 40-45 minutes. Remove from the oven and let cool for 20 minutes. Carefully transfer each dumpling to a small plate and serve.