This is absurdly good for something that is no more than a pile of vegetables wrapped in pastry. And if you have neat fingers and an artistic bent, you can make it look a million dollars, whilst barely making a dent in the bank balance.
Pre-heat the oven to gas 220C/425F/Gas Mark 7.
Bring a large pan of lightly salted water to the boil. Cook the carrot slices for about 5 minutes, then scoop out and drain. Repeat with the potatoes and celeriac, keeping each vegetable separate.
Butter the cake tin generously. Roll out two thirds of the pasty on a lightly floured board to give a rough circle of about 33 cm (13 inches) in diameter. Loosely fold in half and then in quarters, then lift into the tin with the centre tip of the pastry at the centre of the tin. Carefully unfold, then lift the edges and gently push the pastry down to line the sides of the tin using a small knob of pastry rolled into a ball to ease it right into the corner.
Make separate layers of potatoes, carrots and celeriac, sprinkling parsley, caraway seeds, salt and pepper between layers. Dot the vegetables with butter as you go. Roll out the remaining pastry and lay over the pie. Trim off the excess and press the edges of the pastry together firmly. Make a hole in the centre, then let it rest for 30 minutes in the fridge.
Brush the top of the pie with beaten egg and bake for 10 minutes until golden brown. Then reduce the heat to 180C/350F/Gas Mark 4 and cook for a further 50-60 minutes. Test with a skewer to check that the vegetables are cooked and tender. Unmould carefully and serve hot or warm.
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