Heat the olive oil in a large heavy based pan and sauté the leeks, mushrooms and thyme for about 5 minutes or until soft. Add the chicken and the stock and simmer for 5 minutes.
In the meantime, place the butter in a bowl with the flour and mix together to form a beurre manié. Add a tablespoon of the hot stock to the beurre manié and mix well. Add the beurre manié to the pot, stir well and cook for a few more minutes until the stock has thickened.
Remove from the heat, stir in the mascarpone and leave to cool. Use one of the pie bowls upside down as a template and cut out circles of puff pastry, slightly larger than the bowl. Spoon the chicken filling into 4 pie bowls and place the pastry circles on top. Tuck the edges in, make two slits in the middle for with a knife and brush with egg or milk.
Bake in a preheated 200 degree oven for 15 minutes or until the pastry is puffy, golden and crispy.