Melt 1 tablespoon of the butter in a 3- to 4-quart (preferably 8-inch-wide) saucepan over medium-low heat. Add the shallot and cook until softened, about 5 minutes. Add the port and the thyme sprigs and bring to a boil over high heat. Reduce the heat to maintain a brisk simmer and cook until the port has reduced to a syrupy texture, about 30 minutes--you should have about 1/2 cup including the shallot.

Meanwhile, bring the chicken broth to a simmer in a small saucepan. Off the heat, add the porcini and let them soak for 15 minutes. With a slotted spoon, transfer the porcini to a small bowl. Strain the soaking liquid through a fine sieve lined with a paper towel or coffee filter.

Add the soaking liquid and half of the porcini (about 1/3 cup) to the port reduction (save the remaining porcini for the stuffing). Bring the sauce to a boil over high heat. Reduce the heat to maintain a brisk simmer and cook until it has reduced to 1-1/3 cups, about 15 minutes. Strain the sauce through a fine strainer, pressing on the solids. You should have about 1 cup sauce. Set aside until the roast is done.

Soak the currants in hot water for 10 minutes. Drain and put them in a food processor. Add the reserved soaked porcini. Heat 1 tablespoon of the oil in a 10-inch skillet over medium heat. Pat the chicken liver dry and cook on both sides until browned on the outside and just a little pink inside, 3 to 4 minutes total. Transfer to a plate, let cool slightly, and then add to the food processor. Process until finely chopped.

Heat the remaining 1 tablespoon oil in the skillet over medium-high heat. Add the mushrooms, salt, and pepper. Cook, stirring occasionally, until they look wilted and shrunken, 2 to 3 minutes. Add the shallot and garlic and continue to cook, stirring, until the mushrooms are tender and beginning to brown, 3 to 4 more minutes. Add the chicken broth and scrape the bottom of the pan with a wooden spoon to loosen any brown bits. If the liquid doesn't evaporate right away, boil until it does. Remove the pan from the heat and let cool slightly.

Add the sauteed mushrooms, butter, parsley, Cognac or Armagnac, lemon juice, thyme, and lemon zest to the liver mixture in the food processor. Pulse to form a chunky paste and season to taste with additional salt and pepper.

Scrape the stuffing onto a large piece of plastic wrap and shape it into a log a few inches longer than the roast. Tightly roll the stuffing up in the plastic wrap and twist the ends to form a very tight log. Twisting the ends of the plastic will compress the stuffing so that it's just a bit shorter than the roast. Freeze until firm, about 2 hours and up to 2 days.

Trim the silverskin and excess fat from the tenderloin. Butterfly the tenderloin by slicing it lengthwise almost but not completely in half, so that you can open it like a book.

Unwrap the stuffing and center it along one half of the roast. Fold the roast back up to its original shape and tie at 1- to 2-inch intervals with butcher's twine.

Let the roast sit at room temperature for 1 hour (2 hours if the stuffing is frozen solid). Position a rack in the bottom third of the oven and heat the oven to 500 degrees F. Let the remaining 1-1/2 tablespoons butter for the sauce soften at room temperature.

Season the roast generously with salt and pepper and put it on a flat rack set in a roasting pan or heavy-duty rimmed baking sheet. Roast for 15 minutes and then reduce the oven temperature to 325 degrees F. Continue to roast the beef until a meat thermometer inserted into the center of the meat (not the stuffing) registers 125 degrees F for rare or 130 degrees F for medium rare, 30 to 45 minutes more. Move the roast to a carving board and let it rest, loosely tented with foil, for 15 minutes.

While the roast rests, bring the sauce to a simmer in a small saucepan over medium-low heat. Mix the softened butter with the flour to form a paste and whisk it into the sauce. Simmer the sauce to thicken slightly and cook off any raw flour taste, about 3 minutes. Whisk in the vinegar. Season to taste with salt, pepper, and additional vinegar.

Remove the strings from the roast and slice it into 8 to 10 medallions. Put a medallion on each plate and drizzle the sauce around the beef.

Make Ahead: The reduced, strained sauce can be made and refrigerated up to 2 days ahead. If not making the stuffing ahead, refrigerate the remaining soaked porcini separately. The roast can be stuffed and refrigerated up to 1 day in advance.

Drink Suggestions: A hearty red wine with developed tannins, a mineral undertone, and bright fruit pairs well with the earthymushroom and port elements of the beef tenderloin. The Waterstone 2004 Cabernet Sauvignon from Napa Valley would be perfect.