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Trim excess fat from tenderloin. Cut in 6 fillets approximately 7 oz each (200 g). Whole tenderloin can be cooked in oven and cut afterwards.
Combine onions, 2 tablespoons tarragon, vinegar, white wine and pepper in a saucepan. Bring to a boil and cook at low heat until all liquid has evaporated. Remove from fire and reserve. Cool.
Place this mixture in a double boiler over simmering, not boiling water, at low heat. Add yolks and water. Whisk yolks until mixture becomes foamy and thickens. Remove from heat. Whisking constantly, start adding melted butter, cooled to lukewarm. At first, drop by drop, and afterwards in a steady stream until sauce becomes thick and creamy. Add rest of tarragon and parsley and stir. Season with salt and pepper. Set aside over warm water.
For individual fillets, tie kitchen twine around fillets to hold shape while cooking. Heat oil until hot in a skillet and place tenderloins seasoned with salt and pepper. Sear tenderloin about 3 minutes on each side, turn without piercing meat and brown on the other side as desired. Remove twine.
To cook the whole tenderloin: Season meat and sear evenly in hot skillet until brown. Place on a baking pan and cook in preheated oven 400 °F (200 °C) for 20 minutes approximately. Remove from oven and cut in fillets.
Serve sauce over meat together with french fries, Potato Gratin or Creamed Spinach.
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