Preheat oven to 375°. Season beef with salt and pepper to taste. Add meat and 2-3 tablespoons of olive oil to an ovenproof skillet. Set on med high heat. Sear meat for about 3 minutes on each side using tongs to turn. Remove pan from stove top and place in oven. Roast the beef for about 15 minutes for medium rare, 20 minutes for medium and 23 minutes for medium well. Remove from oven and let rest for about 15 minutes. Slice and serve with Bearnaise Sauce.
For the sauce:
In a sauce pan, mix wine, vinegar, shallots, black pepper and reduce it to about 2 tablespoons. Strain mixture and add about 4 drops of cold water. Place mixture in a double boiler on low heat. Cut up the butter, add half of the butter to the mixture and melt. Gradually add remaining butter, stir constantly. Gradually add the beaten eggs a little at a time and stir carefully until mixture thickens. Add a few drops of lemon juice and cold water. Remove from heat and stir in minced tarragon. Use immediately over meat. NOTE: the water in the double boiler should never boil!)