Sift the flour into a shallow freezer-proof bowl, then add small mounds of vegetable shortening.
Add the butter, shake to cover it, then place into the freezer to chill for 20 minutes. (This will make the pastry tender and flaky.)
Mix the orange juice and salt in a separate bowl. Cover and leave in the fridge to chill.
After the 20 minutes, empty the chilled flour and shortening mixture into the bowl of a food processor and pulse to make porridge-like crumbs.
Gradually add the chilled salted orange juice, pulsing until the mixture is just coming together as a dough. Stop just before it comes together (even if some orange juice is left). If all the juice is used up before the dough has begun to come together, add some iced water.
Turn the mixture out onto a clean, floured work surface and, using your hands, knead the mixture to form a dough.
Divide and shape into three equal-sized discs (you'll need to make the mince pies in three separate batches of 12, unless you've got enough tart tins to make all 36 pies at once).
Wrap each disc in cling film and place into the fridge to rest for 20 minutes.
Preheat the oven to 220C/425F/Gas 7.
Remove a pastry disc from the fridge and roll out on a floured work surface thinly, but so that it will be sturdy enough to support the dense mincemeat filling.
Using a fluted pastry cutter, cut out 12 circles a little wider than the moulds in the tart tins. Press the circles gently into the moulds.
Place a teaspoon of mincemeat into each pastry case.
Reroll any remaining dough to a similar thickness, then using a star-shaped cutter, cut out 12 stars and place each lightly onto the mincemeat filling.
Transfer to the oven and bake for 10-15 minutes, or until the pastry is golden-brown. Keep an eye on them as they don't take very long to cook.
Remove from the oven, prising out the little pies straight away and placing onto a wire rack to cool. Allow the empty tray to cool down before repeating the steps from step 10. Repeat until you have made 36 mince pies.