Preheat the oven to 200C/400F. Let the beef come to room temperature.

Trim the wider part of the beef fillet to obtain two pieces of equal width. Tie each piece with kitchen twine, then season with salt and pepper.

Heat a large frying pan over high heat and sear the beef on all sides until golden.

Transfer to the oven and roast for 25 minutes for medium-rare or 30 minutes for well-done. Let rest for 10-15 minutes before serving.

For the sauce, melt the butter in a saucepan until it starts to bubble. Remove from heat and separate the yellow clarified butter from the white sediment.

Blend the egg yolks with white wine vinegar until pale. Gradually add the melted butter, continuing to blend until the sauce thickens and nearly triples in volume.

Stir in the chopped tarragon and season with salt. Keep warm until serving.