Step 1

Prepare the steaks about 1 hour before cooking. Score the fat at 1-inch (2.5 cm) intervals. Grind lots of black pepper over the steaks and sprinkle on a few drops of olive oil. Turn the steaks in the oil and set aside at room temperature.

Step 2

Make the Béarnaise Sauce: In a shallow, heavy-bottom stainless steel saucepan, boil the vinegar, wine, scallion greens, and pepper until completely reduced and the pan is almost dry but not brown. Immediately add 1 tablespoon of cold water. Remove the pan from the heat and let cool for 1 to 2 minutes.

Step 3

Beat in the egg yolks and then add the butter a piece at a time over very low heat, whisking continuously. As soon as one piece melts, add the next piece; the sauce will gradually thicken. If it shows signs of becoming too thick or slightly scrambling, immediately remove from the heat and add a splash of cold water. Do not leave the pan or stop whisking until the sauce is made. Finally, add the tarragon and season to taste. If the sauce is slow to thicken, it may be because you are being too cautious and the heat is too low. Increase the heat slightly and continue to whisk until all the butter is added and the sauce is a thick coating consistency. It is important to remember, however, that if you are making béarnaise sauce in a saucepan directly over the heat, it should be possible to put your hand on the side of the pan at any stage. If the pan feels too hot for your hand, it’s too hot for the sauce.

Step 4

Another good tip if you are making béarnaise sauce for the first time is to keep a bowl of cold water close by so that you can plunge the bottom of the pan into it if it becomes too hot. Keep the sauce warm in a Pyrex bowl over hot but not simmering water or in a Thermos until you want to serve it.

Step 5

Heat the grill pan, season the steaks with a little flaky sea salt, and put them onto the hot pan.

Step 6

The approximate cooking times for each side of the strips steaks are: rare—2 minutes; 
medium rare—3 minutes; medium—4 minutes; and well done—5 minutes. For filet mignon steaks: rare—5 minutes; medium rare—6 minutes; medium—7 minutes; and well done—
8 to 9 minutes. I like to start a strip steak on the fat side and cook until the fat renders out and becomes deliciously crisp, 4 to 5 minutes, then cook on each side to your taste.

Step 7

Transfer the steak to a plate. Let rest for a few minutes in a warm place while you cook the frites.

Step 8

In a deep fryer or large saucepan, heat the oil for deep-frying to about 320°F/155°C. Deep-fry the potatoes until they are almost soft. Drain, increase the oil temperature to 350°F (180°C) to 375°F (190°C), and cook until crisp and golden, another 1 to 2 minutes. Drain on paper towels. Sprinkle lightly with salt.

Step 9

Serve on hot plates with the béarnaise sauce over the steak or in a small bowl on the side and sprinkle over some chopped tarragon. Serve with the frites and watercress. Alternatively, thinly slice the steak, place on a bed of watercress or arugula leaves, drizzle with béarnaise sauce, and serve as soon as possible.