Scoop out the core of the apples, using a melon baller or teaspoon.

In a bowl of a food processor, pulse the walnuts until chopped. Add the butter, brown sugar, vanilla, cinnamon, and salt and process until blended.

Use a small ice cream scoop or spoons to place about a tablespoon of the buttery walnut mixture into the core of each apple. Chill the apples in a sealed container in the refrigerator for about 20 minutes.

Preheat the oven to 400°F. Line a rimmed baking sheet with parchment paper.

On a floured board, roll out pastry dough to about 1/8-inch thickness. Measure your apples and cut out 12 4-inch rounds (this will depend on the diameter of your apples). Place an apple in the center of 1 round and cover with another. Using your finger, moisten the edges with water, then press and seal. Crimp with your fingers or a fork.

Use any remaining dough to form stems and leaves and attach to the dumplings. Repeat with the remaining dough and apples.

Arrange on the lined pan, brush with the beaten egg and sprinkle with cinnamon sugar.

Bake for about 35-40 minutes, or until the pastry is golden brown. Remove from the oven and let cool for 10 minutes.

Carefully transfer each dumpling to a small plate and serve, ideally with vanilla ice cream.