Roughly chop the mushrooms to around 1 to 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. 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.
For the pheasant
While the sauce is cooking, start cooking the pheasant breasts. Pat them dry with kitchen paper and season lightly.
Heat the remaining oil and butter in a clean pan over a medium to high heat and add the pheasant breast. Leave to cook for about 3 minutes then turn over.
Transfer to a plate and keep warm while they rest for 5 minutes.
Serving
Check the seasoning of the sauce and layer at the bottom of the serving dish.
Top with the pheasant breasts and scatter over the remaining tarragon.