Preheat oven to 450 degrees F.
Sear beef filet in skillet in olive oil. Transfer to roasting pan. Roast in oven 15 to 20 minutes or until meat thermometer registers 125 degrees for medium rare. Let stand 15 minutes after removed from oven before carving. Serve filet with sauce.
With hand mixer, cream together 2 sticks softened butter and 2/3 cup Dijon mustard.
In a large saucepan combine 1 1/4 cups shallots, 5 cups white wine and 1/2 cup chopped tarragon. Cook until wine is reduced to 1 cup. The mustard/butter mixture and the shallot mixture may be made 1 day in advance and kept covered and chilled. Reheat the shallot mixture before continuing.
Add 1/3 cup heavy cream and 40 sliced cornichons to wine mixture. Whisk in butter mixture a little at a time. Add any meat juices that have accumulated on platter. Season with salt and pepper, to taste.
Keep warm but do not let boil or sauce will curdle