Preheat your oven to 425°F (220°C).

In a bowl, mix the olive oil, salt, pepper, rosemary, and garlic. Rub this or your beef tenderloin.

Heat a large oven-safe skillet over medium-high heat. Once hot, add the tenderloin, searing it for about 2-3 minutes per side until golden brown.

Transfer the skillet to the oven and roast for about 20-25 minutes, or until a meat thermometer reads 130°F (54°C) for medium-rare.

Once done, remove the tenderloin from the oven and let it rest for at least 10 minutes.

In a small saucepan, combine the white wine vinegar, wine, and shallots. Bring to a gentle simmer and cook until reduced by half.

In a bowl, whisk the egg yolks. Slowly drizzle in the reduced vinegar mixture while whisking.

Place this bowl over a pan of simmering water and whisk in the melted butter until the sauce is rich and creamy. Stir in tarragon, salt, and pepper.

Slice the tenderloin and serve with the Béarnaise sauce drizzled over or on the side.