In a high-speed food processor, add flour and icing sugar. Pulse a couple of times to blend together.
Add chilled cubed butter. Pulse for 15 seconds until mixture resembles coarse crumb.
With processor running, add egg yolk through the shoot and pulse until just combined.
Through the feed shoot, drizzle a tablespoon at a time of the chilled water while pulsing the mixture, until it begins to come together but not a ball of dough. If the dough is still too dry, add a little more water.
Turn dough onto a lightly floured work surface. Bring together and gently knead until it forms a smooth dough ball.
Divide dough in 2 equal halves and flatten each into a round disc. Wrap each in plastic wrap and refrigerate for 30 minutes.
Preheat oven to 180ºC (356ºF). Liberally grease a 12-hole shallow cupcake/muffin pan with melted butter or oil. (Or a specific pan designed for mince pies).
Remove pastry from refrigerator.
Roll out one half pastry on a lightly floured surface or on a sheet of baking paper. Gently roll out to 3mm-5mm in thickness.
Take a round cookie cutter, the same size/large enough to fill moulds in your shallow pan. Cut out enough round bases to fill your pan (12 hole pan). NOTE: if you have extra dough bases cut out but no extra pan, save them and bake another round of pies after your first batch.
Gently push the bases into your shallow greased pan.