Place the shallots, wine, and tarragon vinegar into a non-reactive saucepan. Reduce the liquid, over a low flame until the liquid is less than 1/2 of its original volume (about 3 Tbl). Remove the pan from heat. Allow this reduction to cool to room temperature.
Preheat oven to 400 degrees F.
To assist caramelization, blot the steaks free of moisture with paper towels. Season the surface of one side of the steaks, liberally, with salt and coarsely cracked black pepper. Press the salt and pepper, firmly, into the flesh of the steaks. Dot these sides of the steaks with small chunks of cold butter. Repeat the seasoning and dotting with the other sides of the steaks.
Over a medium flame, heat up two heavy 10 or 12 inch aluminium skillets.
In the skillets, sear both sides of the steaks. Place the skillets into the oven and roast the meat until it reaches NO MORE than medium-rare in doneness. This procedure will take only a few minutes (8-10 minutes in the oven may turn the steak into a piece of rubber, ruining an excellent cut of beef!). Remove the pan from the oven and the steaks from the pan. Tent the steaks under aluminium foil. While the steaks rest, prepare the Sauce Choron.
Break the eggs and separate the whites from the yokes. Make sure that the clarified butter is warm, but not scaldingly hot. In a sauteuse over a VERY low flame, throw the shallot reduction into the pan. Sprinkle in the cayenne. Add the egg yokes, whisking them constantly until they achieve a ribbon-like consistency. (When it appears that the heat is increasing too fast, move the pan off the burner to prevent the eggs from scrambling.) Add the clarified butter - drizzling a ladle at a time and whisking until the sauce comes together. It should closely resemble the texture of mayonaise. Cut off the heat, add the tomato product and salt to taste. Keep this sauce warm. If reheated, it will break.
Bring the skillet that the rib steaks were cooked in up to heat over a medium flame. De-glaze the skillet with 1/2 cup of Bordeaux. Pour whatever juices have accumulated under the steaks into the skillet. Reduce the liquid until the sauce turns into a thick glaze.
Transfer the steaks to a large serving platter. Drizzle the wine reduction and Sauce Choron over the steaks - in a spiraling or a criss-cross artsy-pattern. (If you are not too exhaused after the labor expended in making this dish, eat a steak.)