For the Hollandaise sauce: Whisk the egg yolks and lemon juice in a stainless steel bowl until the mixture is thickened, pale and doubled in volume, for about 5 minutes. Place the bowl over a saucepan containing barely simmering water or use a double boiler. Cook's Note: The water should not touch the bottom of the bowl.
Continue to whisk rapidly. (See Cook's Note)
Slowly drizzle the melted butter and continue to whisk until the sauce is thickened. Remove from heat. Add the Dijon mustard and tarragon. Season the sauce with salt and pepper. Keep warm until ready to serve. If the sauce gets too thick, whisk in a few drops of warm water before serving.
For the rib steak: Preheat the oven to 350 degrees F/180 degrees C. Season the steaks with salt and pepper. Heat a large oven-proof heavy skillet on high and add oil. Add the steak, cooking until crispy on both sides, 6 minutes in total.
Place the skillet in the oven for another 8 minutes for medium-rare. During the last 2 minutes, add the butter and continue cooking.
Remove the steak and let rest, covered with aluminum foil to keep warm.
For the asparagus: Boil the asparagus for about 45 seconds, until slightly cooked. Remove the asparagus from the heat and plunge into a bowl of ice-cold water. Meanwhile, in a medium pan heat the butter until it melts. Add the shallots and asparagus, cook another 2 minutes over medium heat. Season the asparagus with salt and pepper. Keep warm.
Serve the steak with the buttered asparagus, hollandaise sauce and fries, if desired.
Be careful not to let the eggs get too hot or they will scramble.