Recipe(tried): Chateaubriand with Bearnaise

Ch teaubriand with B arnaise (Perfect for the Holidays)
From The French Recipe Cookbook by Carole Clements and Elizabeth Wolf-Cohen.
(Ch teaubriand is a lean and tender cut from the thick center of the fillet that is pounded to give it its characteristic shape. It is usually served for two, but could easily stretch to three.)

2/3 cup butter, cut into pieces
1 1/2 Tbsp tarragon vinegar
1 1/2 Tbsp dry white wine
1 shallot, finely chopped
2 egg yolks
1 pound beef fillet, about 5 to 6 inches long, cut from the thickest part of the fillet
1 Tbsp vegetable oil
salt
freshly ground black pepper
saut ed potatoes, to accompany

Clarify the butter by melting it gently in a saucepan; do not boil. Skim off any foam and set aside.

Put the vinegar, wine and shallot in a small heavy saucepan over high heat and boil to reduce until the liquid has almost all evaporated. Remove from the heat and cool slightly. Add the egg yolks and whisk for 1 minute. Place the saucepan over very low heat and whisk constantly until the yolk mixture begins to thicken and the whisk begins to leave tracks on the base of the pan, then remove the pan from the heat.

Whisk in the melted butter, drop by drop until the sauce begins to thicken, then pour in the butter a little more quickly, leaving behind the milky solids at the bottom of the pan. Season with salt and pepper and keep warm, stirring occasionally.

Place the meat between two sheets of wax paper or plastic wrap and pound with the flat side of a meat pounder or roll with a rolling pin to flatten to about 1-1/2 inches thick. Season with salt and pepper.

Heat the oil in a heavy frying pan over medium-high heat. Add the meat and cook for about 10 to 12 minutes, turning once, until done as preferred (medium-rare meat will be slightly soft when pressed, medium will be springy and well-done firm).

Transfer the steak to a board and carve in thin diagonal slices. Strain the sauce, if you prefer, and serve with the steak, accompanied by saut ed potatoes. Yield: serves 2