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Mix the egg yolks with the mustard powder, pepper, 1 tbsp cider vinegar and a pinch of salt in a bowl. Mix the oils together in a jug. Use an electric whisk to whisk the yolk mixture, then very slowly, drip-by-drip, add the oil. When the mixture is pale and thicker, and no oil is visible, swap from a drip to a slow, steady stream – whisking all the while.
When all the oil is added and you have a thick mayonnaise, taste and season with more vinegar, salt and pepper. Stir in the lemon zest and chives, then chill until ready to serve.