Lie the chicken in a saucepan in a single layer and cover with the stock. Heat until the stock has just come up to the boil then immediately turn the heat down to a gentle simmer.
Poach the chicken until it is cooked through, about 12 minutes. (Check the chicken is cooked by piercing it with a very sharp knife – the juices should be clear, with no trace of pink).
Leave the chicken to cool in its cooking liquor so that it stays moist.
To make the dressing, mix the vinegar, mustard and salt and pepper in a cup. Whisk in the oil, water and cream. Add the tarragon and sugar. Mix and taste.
You may want to adjust the seasoning or the sweetness. The consistency should be that of single cream. This dressing improves while it sits as the tarragon flavour gets stronger, so cover and leave for half an hour or so.
Cut the chicken into neat slices and gently toss with the cherries, watercress, pistachios and dressing. Serve straight away.
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Diana Henry is the author of A Bird in the Hand.