In a large mixing bowl, whisk together the all-purpose flour, salt, and granulated sugar until combined. Cut in the cold, unsalted butter until the mixture resembles coarse crumbs. Gradually add cold water, mixing until the dough forms. Divide the dough into two discs, wrap in plastic wrap, and refrigerate for at least 30 minutes.

In a separate bowl, combine diced apples with sugar, cinnamon, nutmeg, lemon juice, and flour. Toss until evenly coated and let sit for 10 minutes.

Preheat the oven to 375°F (190°C). Roll out one disc of chilled dough to about 1/8 inch thick. Cut out circles larger than your muffin tin cups for the base of the pies.

Place the dough circles into the greased muffin tin and fill each with the apple mixture. Roll out the second disc of dough and cut smaller circles or shapes to place on top. Seal edges and brush tops with egg wash.

Bake the Mini Apple Pies for 20-25 minutes until golden brown and filling bubbles slightly. Allow to cool for a few minutes before serving warm.