Preheat the oven to 400 degrees F.
Season the beef with salt and pepper. In a large skillet, over high heat, melt the butter. Add the beef and sear for a couple of minutes on each side. Place in the oven and roast for 20 to 25 minutes for medium rare. Remove from the oven and rest for 5 minutes before slicing.
FOR THE POTATOES:
In a sauté pan, over medium heat, melt 8 tablespoons of butter. Add the potatoes and season with salt and pepper. Saute the potatoes for 3 to 4 minutes. Place the potatoes in the oven and roast the potatoes until golden brown and tender, about 20 minutes, shaking the pan every 5 minutes. Remove from the oven and add the parsley.
FOR THE SAUCE:
In a saucepan, combine the vinegar, wine, peppercorns, shallots, and tarragon. Bring the liquid to a boil and reduce to 1 tablespoon. Add 1 tablespoon of water. Combine the reduced liquid and egg yolks in a stainless bowl, over simmering water. Whisk until frothy. In a steady stream, add the butter until the sauce thickens. Season with salt and pepper. Strain the sauce through a chinois and set aside.