Step 1: Make the Pie Crust
In a large bowl, whisk together flour, sugar, and salt. Add cold butter cubes and use a pastry cutter or fork to cut the butter into the flour until the mixture resembles coarse crumbs. Add ice water one tablespoon at a time, mixing until the dough comes together. Divide dough in half, shape into discs, wrap in plastic wrap, and refrigerate for at least 30 minutes.

Step 2: Prepare the Apple Filling
While the dough chills, combine diced apples, both sugars, lemon juice, cinnamon, nutmeg, and cornstarch in a medium saucepan. Cook over medium heat for 5-7 minutes, stirring occasionally, until apples soften slightly and the mixture thickens. Stir in butter until melted. Remove from heat and let cool completely.

Step 3: Preheat and Prep
Preheat your oven to 375°F (190°C). Grease a 12-cup muffin tin or line with parchment paper circles for easy removal.

Step 4: Roll and Cut the Dough
On a lightly floured surface, roll out one disc of dough to about ⅛-inch thickness. Use a 4-inch round cutter to cut 12 circles for the bottoms. Press each circle gently into the muffin cups. Roll out the second disc and cut 12 smaller circles (about 3 inches) or use cookie cutters for decorative tops.

Step 5: Fill the Pies
Spoon about 2 tablespoons of cooled apple filling into each pastry-lined muffin cup. Don’t overfill or the filling may bubble over during baking.

Step 6: Add the Top Crust
Place the smaller dough circles on top of each filled pie. Press edges gently to seal, or crimp with a fork for a decorative edge. Cut small slits in the top of each pie to allow steam to escape. Brush tops with beaten egg and sprinkle with coarse sugar if desired.

Step 7: Bake
Bake for 22-25 minutes, or until the crust is golden brown and the filling is bubbling. Remove from oven and let cool in the pan for 10 minutes.

Step 8: Remove and Serve
Carefully remove the mini apple pies from the muffin tin using a butter knife or small offset spatula. Let cool on a wire rack for at least 15 minutes before serving. Serve warm or at room temperature.