How to Make It
In a large saucepan, melt the duck fat. Add the short ribs and cook over moderate heat until browned all over, about 10 minutes; discard the fat. Add the garlic and the 4 shallots and cook, stirring, until lightly browned, about 5 minutes. Add 1 quart of stock and simmer over low heat until reduced by half, about 1 hour. Add the remaining 1 quart of stock and simmer until reduced to 1 1/2 cups, about 2 hours. Strain, skim the fat and season with salt.
In another large saucepan, melt 2 tablespoons of the butter. Add the 1 pound of sliced shallots and cook over low heat, stirring occasionally, until softened, about 8 minutes. Season with salt, add the wine and cook until the shallots are meltingly tender and the liquid is absorbed, about 1 hour. Season the marmalade with pepper.
Preheat the oven to 350°. In a large ovenproof skillet, melt 1 tablespoon of the butter. Add the mushrooms, season with salt and pepper, cover and cook over low heat until nicely browned, about 4 minutes. Transfer the mushrooms to a plate; wipe out the skillet.
Using a paring knife, make 4 dozen incisions all over the tenderloin about 1/2 inch apart. Push an olive, pistachio or mushroom strip into each incision, alternating the flavorings. Using cotton string, tie the tenderloin at 2-inch intervals.
Melt the remaining 3 tablespoons of butter in the skillet. Season the beef with salt and sear on 3 sides over moderately high heat, until browned, about 9 minutes. Turn the roast uncooked side down, transfer the skillet to the oven and roast for 10 minutes. Baste the tenderloin with the pan juices and cook for about 6 minutes longer, or until an instant-read thermometer inserted in the center registers 120° for rare. Transfer the roast to a cutting board and season with pepper. Cover loosely with foil and let stand for 10 minutes. Discard the fat from the skillet.
Rewarm the shallot marmalade and beef jus. Add 1 cup of the jus to the skillet and bring to a boil, scraping up the browned bits. Pour the remaining jus into a gravy boat. Strain the pan juices into the gravy boat.
Slice the roast 1/2 inch thick. Mound a little shallot marmalade in the center of each plate and arrange 3 slices of the beef alongside the marmalade. Spoon a little beef jus onto the beef and pass the remaining jus separately.