Sort through wild mushrooms brushing any dirt from mushrooms. Trompets will have to be washed as they have a lot of dirt on the inside.
Sweat shallots and thyme in a little of the butter and oil and then add the girolle mushrooms and cook gently. Remove from the pan and cook all the other mushrooms separately in the remaining olive oil and butter.
Place all the mushrooms in a sieve and drain to remove any liquid. Finish with salt and pepper and freshly chopped tarragon.