Heat a tablespoon of oil in a deep frying pan. Slice the chicken breasts in half diagonally, season with salt and pepper and fry skin side down for a few minutes until golden. Turn over and cook for one minute more. Keep to one side.
Finely slice the onions and fry in the same pan for five minutes until soft and slightly coloured. Skin and slice the mushrooms, add these to the pan and cook for two more minutes, adding a little more oil if needed.
Pour in the white wine and simmer until slightly syrupy. Add the cream, mustard, half of the tarragon leaves and a little salt and pepper. Stir well, bring to a gentle simmer and return the chicken pieces to the pan skin side up. Place a lid on top and cook gently for ten minutes until the chicken is cooked through.
Taste and adjust the seasoning before serving with the remaining tarragon scattered on top.
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