Preheat the oven to 140°C. Season the beef with salt & pepper.
Place a large frying pan on a medium heat and when it is really hot add the olive oil and carefully place the beef in the pan. Sear the meat on all sides to give it a nice brown colour.
Transfer the beef to a roasting tray and place in the oven.
Using a meat thermometer to monitor the internal temperature of the meat. Remove the beef from from the oven once an internal temperature of 54°C is reached. Allow the beef to rest in a warm place for 15 minutes.
For the Bernaise Sauce:
Combine the whole butter and clarified butter, melt and keep warm.
Bring a pot of water to a simmer. Combine the egg yolks, water and chardonnay wine in a mixing bowl over the pot of simmering water and remove pot from the heat. Whisk continuously, pour in the melted butter in a thin stream, until combined.
Mix in the chopped tarragon and salt.
Preheat the oven to 200°C. Just before serving return the beef to the oven for 2 minutes to reheat.