Prepare the Pie Crust:
In a large mixing bowl, whisk together the flour, salt, and sugar.
Add the cubed butter to the flour mixture. Using a pastry cutter or your fingers, work the butter into the flour until it resembles coarse crumbs.
Gradually add the ice water, one tablespoon at a time, mixing with a fork until the dough begins to come together.
Turn the dough out onto a lightly floured surface and knead it gently until it forms a smooth ball. Flatten the ball into a disc, wrap it in plastic wrap, and refrigerate for at least 30 minutes.
Prepare the Filling:
In a large mixing bowl, combine the diced apples, granulated sugar, brown sugar, flour, cinnamon, nutmeg, salt, and lemon juice. Toss until the apples are evenly coated.
Assemble the Pies:
Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper.
On a lightly floured surface, roll out the chilled pie dough to a thickness of about 1/8 inch. Using a round cookie cutter or the rim of a glass, cut out circles of dough that are slightly larger than the openings of your mini muffin tin.
Gently press each dough circle into the wells of the mini muffin tin, forming small pie crusts.
Fill each pie crust with a spoonful of the apple filling, pressing it down lightly to pack it in. Top each pie with a small piece of diced butter.
Top and Bake the Pies:
Roll out any remaining pie dough and cut it into thin strips. Arrange the strips in a lattice pattern over the tops of the mini pies, trimming any excess dough as needed.
Brush the tops of the pies with beaten egg, then sprinkle them with granulated sugar.
Place the mini muffin tin in the preheated oven and bake for 18-20 minutes, or until the crust is golden brown and the filling is bubbling.
Remove the pies from the oven and allow them to cool in the muffin tin for 5 minutes before transferring them to a wire rack to cool completely.
Serve and Enjoy:
Once cooled, carefully remove the mini apple pies from the muffin tin and serve them warm or at room temperature. Enjoy them as a delightful sweet treat or dessert for any occasion!