Remove puff pastry from the freezer and thaw according to package instructions.
In a medium sauce pan over medium heat, place water, sugar, cornstarch, cinnamon, nutmeg, and salt. Whisk until there are no more clumps of corn starch. Then, bring mixture to a boil, stirring frequently for about 2-3 minutes.
Once the mixture has boiled for 2 minutes, add the peeled and diced apples, cover, and let simmer until the apples are soft or about 4-5 minutes.Remove from heat and let the mixture cool completely.
Preheat oven to 400˚F.
Using a pizza cutter or a knife, cut each pastry sheet into 9 sections. You should have 18 total. The easiest way to do this is cut 2 horizontal lines where the puff pasty sheets have a crease and then 2 vertical lines, slightly over 3″ apart. Add about 1-2 tablespoon of the apple filling and about 1 teaspoon of chopped walnuts on 9 of the puff pastry sections, leaving about ⅛ inch space around the edges.
Brush the edges of the puff pastry with egg wash and add a puff pastry sheet on top of each of the 9 filled with apple pie filling and walnuts. Crimp tightly around the edges to seal the turnovers.
Transfer to a baking sheet lined with parchment paper, keeping them at least 1″ apart. Brush each of the turnovers with egg wash and sprinkle granulated sugar on top. Bake 20-23 minutes or until golden and puffy.
Transfer apple walnut turnovers onto a cooling rack and allow to cool.