Preheat oven to 275F. Use oven thermometer to maker oven temp is accurate.

Place filet on sheet pan and pat dry all over with paper towels. Brush filet all over with oil, reserving 1/2 T. Sprinkle filet all over with salt and pepper.

Place tarragon branches around beef, tying them in 4,5 places with kitchen twine to keep them in place. Brush tarragon with remaining oil.

Roast filet of beef 1 1/4 - 1 1/2 hrs, until temp registers 125F in center for rare, and 135F for medium rare.

Cover filet with foil and allow to rest 20 min. Slice thickly ad serve warm or at room temp.