Using a thin knife, trim and discard the excess fat and all of the silver skin from the tenderloin. Remove the long "chain" meat that runs next to the tenderloin and reserve for another meal. Part of the thin “tail” end of the tenderloin may separate as it is trimmed, but leave it connected to the main muscle as much as possible. Lay the tenderloin out flat and straight, with the smoothest side up, aligning the narrow pieces at the tail end. Neatly fold the tail end of the tenderloin under itself to form an even thickness (one end may be larger). Tie the roast snugly with butcher’s twine at 2-inch intervals. Secure the folded end with two strings. Lightly coat the roast with oil. Season the roast all over with the rub.
Let the roast stand at room temperature for 30 minutes to 1 hour before grilling.
Prepare the grill for indirect cooking over medium heat (350° to 450°F).
In a large skillet over high heat on the stove, combine the shallot, vinegar, tarragon, and thyme, and cook until the vinegar evaporates, 3 to 4 minutes, stirring often. Add the wine and broth and boil until reduced to about ½ cup, 3 to 4 minutes. Add the cream and boil until the surface is covered with large, shiny bubbles and the sauce is reduced to about 1½ cups, 5 to 7 minutes. Remove from the heat, adjust the seasonings, and set aside. Reheat and add parsley just before serving.
Related Grill Skills
Brush the cooking grates clean. Sear the roast over direct medium heat for about 15 minutes, turning a quarter turn once every 3 to 4 minutes. Then slide the roast over indirect medium heat and cook until it reaches your desired doneness, 20 to 30 minutes for medium rare (125º to 130ºF), turning once. Keep the lid closed as much as possible during grilling. Remove from the grill, loosely tent with foil, and let rest for 10 to 15 minutes. The temperature will rise a few degrees during this time.
Snip and remove all the twine from the roast. Cut the meat crosswise into ½- to 1-inch slices. Season with salt. Serve warm with the sauce.