Puree the egg, sugar, mustard powder and salt and pepper in a food processor until smooth. Add the oil, pouring in a steady stream, and puree until the mixture is very thick and all the oil has been incorporated.
Add the juice of the lemon and puree again. Transfer to a bowl and stir in the gherkins, capers, parsley and tarragon.
Cover and leave for 1 hour to allow the flavours to blend.
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