Rib-eye steak with Bearnaise sauce

First make the Bearnaise sauce. Remove the tarragon leaves from the stems. Finely chop the stems and set aside, then chop the leaves and set aside. Combine the vinegar with 2 tablespoons of water, the tarragon stems, pepper and shallot in a saucepan. Bring to the boil. Reduce for a few minutes, strain off the liquid and set aside. In a second saucepan, melt the butter over a low heat. In another saucepan, beat the egg yolks with the vinegar for 5 minutes over a very low heat, until the mixture starts to bind. Add the warm butter and keep beating. Season with cayenne pepper and stir in the chopped tarragon leaves. Set aside.Bring the meat to room temperature. Season the steaks with salt and pepper. Preheat the pan. Melt a small teaspoon of butter (rib-eye steak is already relatively high in fat), allow the butter to color and then fry the steaks over a medium heat: 3 minutes for rare, 4 minutes for medium rare or 5 minutes for medium. Remove the steaks from the pan, wrap them in aluminum foil and leave to rest for 5 minutes. Serve with the Bearnaise sauce.