Prepare the Beef: Preheat the oven to 200°C (400°F). Allow the beef to come to room temperature. Trim and tie the beef fillet for even cooking. Season generously with salt and pepper.

Sear the Beef: Heat a large frying pan over high heat. 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 slicing.

Make the Bearnaise Sauce: Melt butter in a saucepan until it starts to bubble. Remove from heat and separate the clarified butter from the sediment. In a blender, mix egg yolks with white wine vinegar until pale. Gradually add melted butter, blending until the sauce thickens and nearly triples in volume. Stir in chopped tarragon and season with salt. Keep warm until ready to serve.

Serve: Slice the rested beef and serve with the warm Bearnaise sauce.