Preheat the oven to 225°C.
Place a heavy baking tray into the oven to preheat.
Mix flour, salt, and icing sugar in a bowl, then add the egg into a central well and cover with flour.
Bring water, butter, and lard to a slow boil in a saucepan over low heat.
Stir the boiling liquid into the flour and knead on a floured surface until smooth.
Roll two-thirds of the pastry to line a 25cm loose-bottomed cake tin with a 2cm overhang.
Roll out the remaining third of the pastry to create the lid.
Fry leeks and thyme in butter for 5-8 minutes until tender and allow to cool.
Pulse lamb, parsley, and mint in a food processor and season with salt and pepper.
Layer the lamb and then the leeks into the pastry case.
Seal the pastry lid onto the case by brushing edges with egg and crimping.
Trim excess pastry and use trimmings to create decorative leaves.
Brush the top with egg, make a steam hole in the center, and attach pastry leaves.
Bake at 225°C for 15 minutes, then reduce to 180°C and bake for one hour.
Cool for five minutes before serving with cooked potatoes and carrots.