Make the potato pastry. Finely grate the potatoes, then pat dry between several layers of kitchen paper. Place the flour in a bowl, add the salt, butter and lard and rub in with the fingertips until the mixture resembles coarse breadcrumbs. Mix in the potatoes. Mix the mustard with 1 tablespoon cold water in a cup, add to the bowl and mix to a firm dough with a round-bladed knife, adding a dash more water if the dough feels dry and crumbly. Wrap and chill for at least 30 minutes.
Check over the fish for any stray bones, then cut into small chunks. Toss with the cornflour in a small bowl and scatter into a shallow ovenproof dish or pie dish. Push the eggs down between the pieces of fish.
Scatter the spring onions, peppercorns, parsley and peas into the dish and spoon the sauce on top. Roll out the pastry on a lightly floured surface until slightly larger than the dish. Brush the rim of the dish with water and lay the pastry over, trimming off the excess. Crimp the pastry edges and make a hole in the centre. Brush with beaten egg and sprinkle with salt. Bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 20 minutes. Reduce the temperature to 160°C (325°F), Gas Mark 3, and cook for 40 minutes until the pastry is deep golden.