Preheat the oven to 200°C, fan 180°C, gas 6.
Put the carrots and celeriac in a large pan and pour over the stock. Bring to the boil then reduce to a simmer for 15 minutes. Drain, but reserve 200ml of the cooking stock. Set aside.
Melt the butter in a medium saucepan and add the onion and leeks. Cook gently for 5-10 minutes until softened. Stir in the flour and cook for a further minute. Gradually stir in the milk.
Add the reserved vegetable stock and the parsley then bring to a simmer, stirring, until the sauce has thickened slightly. Add the cooked carrots and celeriac, and the pork. Stir until combined then spoon into a 2-litre pie dish.
Unroll the pastry and cut it into long thin strips.
Brush the lip of the pie dish with a little of the beaten egg, then press down a strip of pastry around the edge to cover it. Brush the pastry with more egg, then weave the other pastry strips under and over each other, pressing down at the edges, to make a lattice effect.
Brush the pastry lattice all over with the remaining beaten egg and bake for 25-30 minutes, until the pie filling is bubbling and the pastry is golden.