Preheat the oven to gas 6, 200°C, fan 180°C.
In a large frying pan, melt 15g butter with 1 teaspoon oil over a high heat. Add the mushrooms and cook briskly, stirring often, for 2-3 minutes. Stir in the garlic and cook for 2 minutes more. Transfer to a mixing bowl and return the pan to a low heat. Add the remaining 15g butter and teaspoon of oil, followed by the chopped onion and thyme and cook gently for 15 minutes until soft, but not coloured.
Add the flour, stir over a medium heat for a minute then gradually add the stock, stirring to form a smooth sauce. Bring to the boil and simmer for 5 minutes until thickened. Remove from the heat and stir in the crème fraiche, chicken and reserved mushroom mixture. Season to taste and spoon into an ovenproof dish.
Brush the edge of the dish with water and run a 1-2cm wide strip of pastry around it, cut from the edge of the pastry sheet. Lay the remaining pastry over the dish and trim the edges with a sharp knife, leaving a 2-3cm overhang. Trim and crimp the overhang. Beat the egg with the milk to make a glaze and brush over the pastry. Make two slits in the centre to release the steam. Bake for 20-25 minutes until the pastry is golden and risen and serve with steamed greens.
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