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Put the egg yolks in a mini food processor and season with salt, pepper and a pinch of cayenne, then add the vinegar.
Finely chop the tarragon stalks and leaves separately. Melt the butter in a pan then add the chopped tarragon stalks and bring it to a simmer – the butter needs to be hot so that it will cook the egg yolks slightly.
Turn the processor on and add the hot melted butter slowly while the processor is running. Once all the butter has been added and the mixture is smooth and thick, pour it into a bowl and stir through the tarragon leaves. Season and serve with steak.