Heat a large skillet with olive oil over high heat. Sprinkle the steaks with salt and pepper and place in a preheated pan. Fry for about 3-4 minutes on each side. Transfer the finished steaks to a cutting board, cover with foil and let rest for 5-8 minutes.
In the meantime, prepare the beef steak sauce. In a small saucepan, combine the shallots, vinegar, and tarragon put on medium-high heat, and cook, stirring occasionally, for 3-4 minutes.
Meanwhile, pour some water into another pot to form a steam bath. Bring water to a boil and simmer over low heat.
Combine yolk, broth, and starch in a small heatproof bowl. Add the contents of a saucepan to this bowl, stir well and place over a saucepan of boiling water. Increase the heat under the pan and cook the sauce on the steam bath, stirring constantly, until thickened, 3-4 minutes. Then remove the bowl from the bath and add salt and pepper to the sauce to taste.
Cut the meat into slices and serve the beef with sauce.