Preheat the oven to 200°C.
Slice a pocket into the chicken breast and stuff with tarragon and Stilton.
Season with salt and pepper and wrap tightly in two layers of clingfilm.
Bring a pan of water to a boil and reduce to a gentle simmer.
Poach the chicken parcel in the simmering water for 12-14 minutes.
Remove the chicken with a slotted spoon and keep it warm.
Drizzle large mushrooms with olive oil and roast in the oven for 6-8 minutes.
Sauté the chopped onion in olive oil and butter until soft.
Add the chopped mushroom and sauté for another 2-3 minutes.
Pour in the wine and simmer until the liquid is reduced by half.
Stir in the cream and simmer until the sauce thickens slightly.
Mix through the remaining tarragon.
Unwrap the chicken and slice it into three medallions.
Place the medallions over the roasted mushrooms and pour over the sauce.