How to Make It
Preheat the oven to 350°. In a mortar or mini processor, pound or pulse the garlic to a paste. Add the anchovies and pound or pulse until smooth. Stir in the minced rosemary and thyme and 2 tablespoons of the olive oil.
Spread the saddle of lamb on a work surface, fat side up. Using a sharp knife, lightly score the fat in a crosshatch pattern. Turn the saddle over and trim any excess fat from the loin, tenderloin and flap pieces. Season the lamb with salt and pepper. Rub the anchovy-herb filling over the inside of the lamb. Roll up the roast, wrapping the flaps around the outside to form a neat cylinder, then tie at 1-inch intervals with kitchen string. Season the outside of the roast with salt and pepper.
In a very large, ovenproof skillet, heat 1 tablespoon of the olive oil. Add the lamb roast and cook over moderately high heat until nicely browned all over, about 10 minutes. Transfer the skillet to the oven and roast the lamb for about 1 hour, or until an instant-read thermometer inserted into the center of the roast registers 120°. Transfer to a carving board and let rest for 15 minutes.
Pour the skillet juices into a small saucepan and skim off the fat. Add any juices that have collected around the roast. Add the water and bring to a simmer. Stir in the remaining 2 teaspoons of olive oil and the balsamic vinegar and season with salt and pepper. Strain the jus through a fine sieve into a warmed gravy boat.
Cut and discard the strings from the roast. Thickly slice the roast crosswise and serve with the jus.