Peel and finely chop the shallots. Chop the mushrooms into slices or pieces of 1 or 2 centimetres.
Strip the tarragon leaves from the stems and chop.
Put the oil and butter in a pan over a medium heat. Add the shallots and cook for 2 minutes until soft, but not coloured, and stir occasionally with a wooden spoon.
Add the mushrooms to the pan. Cook and stir occasionally for 5 minutes until the mushrooms are soft.
Pour in the stock and cook for a further 5 minutes until the liquid has reduced.
Add the cream and half of the tarragon and simmer gently until the sauce has thickened.
Add the salt and pepper and check the seasoning. Stir in most of the chopped tarragon and scatter the rest on top to serve.