Heat oil in a deep saucepan and the fry onion, leek and garlic until they begin to caramelise, stirring occasionally. Add kumara and cook 1 minute then tip into a bowl.
Place saucepan back on the heat and add a little more oil. Add lamb and brown on all sides. Sprinkle flour in and mix, then add leek mixture, herbs, beans, meat stock and enough water to cover the meat by 2 cm (¾ in. Bring to the boil, turn to a simmer and cook, covered, for 90 minutes. Remove lid and keep cooking until most of the liquid has evaporated, stirring occasionally. Check seasoning and cool completely, then place in the fridge to go cold.
Preheat the oven to 190°C/375°F/Gas Mark 4. Roll pastry into a rectangle about 30 × 40 cm (12 × 16 in) and ½ cm (¼ in) thick. Place on a lightly floured baking tray and brush it all over with beaten egg. Spoon chilled mixture along one half of the pastry, leaving a 3 cm (1 ¼ in) border. Fold pastry over filling and seal the edges by pressing with a floured fork. Brush top with more egg and prick all over with a fork. Bake for 35-40 minutes until dark golden brown.