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The first thing to do is to make a thick white sauce that will be the base of the turnover filling. Bring the milk to a simmer, then add the butter and flour paste. Whisk the paste into the simmering milk and allow it to boil for 3-4 mins, whisking gently all the time to prevent it from catching. You should now have a very thick white sauce. Cool the sauce in a bowl. Fry the mushrooms in the oil for 3-5 mins until golden, then leave to cool.
Place the ham, cheese and mushrooms into a bowl, then gradually add the white sauce until everything is well coated. Finally, add the herbs.
Roll out the pastry on a floured surface to about the thickness of a £1 coin and cut out 4 saucer-size rounds (about 18cm wide), re-rolling the trimmings if you need to. Brush the edges of each round with beaten egg. Spoon the mixture onto 1 side of each round, then fold over and seal the edges well. The turnovers can now be frozen for up to 1 month. Brush the turnover with the remaining egg, then chill for 30 mins.
Heat oven to 200C/180C fan/gas 6. Place the turnovers on a baking sheet and bake for about 35 mins until puffed up and golden. Leave to cool slightly and enjoy warm.