Finely chop the shallot, tarragon, and chives for easy incorporation into the sauce.
In a small saucepan, combine the white wine vinegar, water, chopped shallots, and a pinch of salt. Bring to a simmer and cook until the liquid has reduced by about half.
Strain the vinegar and shallot reduction and let it cool slightly.
In a heatproof bowl, whisk the egg yolks. Place the bowl over a simmering pot of water (double boiler) and gradually whisk in the vinegar reduction.
Melt the butter. While continuously whisking the egg yolk mixture, slowly drizzle in the melted butter to create a smooth and emulsified sauce.
Stir in the chopped tarragon and chives. Season with salt and pepper to taste.
Serve immediately with steak, grilled meats, or vegetables for a classic French culinary experience.
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