1    Beef Fillet; About 5 Pounds
1/2 c  (1 Stick) Butter
1 tb Minced Fresh Tarragon; OR
1 ts Dried Tarragon; Crushed
1 tb Minced Fresh Chervil; OR
1 ts Dried Chervil; Crushed
1 tb Minced Shallots Or Scallions
2 tb Dry White Wine
2 tb White Wine Vinegar

Buy a prime fillet, if possible, and fold under and tie the tail to form a
roast of uniform thickness. Melt the butter in a small saucepan. Stir in
the tarragon, chervil, and shallots or scallions. Cook over very low heat
for a minute or two. Slowly stir in the wine and vinegar and heat slowly.
Place the meat on a tray and brush with the herbed butter. Let stand at
room temperature for 1 hour, brushing with the sauce 2 or 3 times more.
Remove the meat from the tray and pour any sauce remaining on the tray into
the saucepan with the remaining sauce. Brown the fillet over the coals on
all sides for about 10 minutes, watching carefully to prevent any fire
flareups. Move the meat to the edge of the grill or cover the grill and
adjust the dampers to maintain slow steady heat. Grill 15 to 20 minutes
longer or until the fillet is done as desired. Heat the remaining sauce at
the edge of the grill and serve with the sliced fillet.