Pulse flour, sugar, and salt in a food processor, then add cold cubed butter and pulse 10–12 times until the mixture resembles coarse breadcrumbs with some pea-sized pieces remaining.
Whisk the egg yolk with 3 tablespoons of ice water, then pour slowly into the running food processor and process just until the dough begins to clump together; add the remaining tablespoon of water if needed.
Turn dough onto a work surface, bring together gently without overworking, divide into a 60/40 split, flatten each into a disk, wrap in plastic wrap, and refrigerate for at least 30 minutes or up to 2 days.
Preheat your oven to 400°F (200°C) and lightly grease a muffin tin with butter or non-stick spray, paying special attention to the corners.
On a lightly floured surface, roll the larger portion of dough to about 1/8 inch thickness, then cut out circles using the 3-inch cutter and press each into a muffin cup so it fits snugly up the sides.
Spoon 1–2 teaspoons of mincemeat filling into each pastry-lined cup, filling about three-quarters full, then level gently with the back of your spoon — do not overfill.
Roll out the second dough portion to 1/8 inch thickness, cut circles with the 2.5-inch cutter, place on top of each filled pie, and press edges to seal; cut a small slit or cross in each top to allow steam to escape.
If desired, brush the tops of the pies with a little milk or beaten egg for extra golden color before baking.
Bake in the preheated oven for 18–20 minutes until the pastry is golden brown and crisp, and the filling is just beginning to bubble through the steam vents.
Let the pies cool in the tin for 5 minutes, then transfer to a wire rack, allow to cool 10–15 minutes more, and dust generously with powdered sugar before serving warm or at room temperature.