Position a rack in the lower middle of the oven and heat the oven to 450°F. Trim any excess fat from the lamb. With the point of a knife, make 16 slits all over the lamb and insert a sliver of garlic into each slit. Sprinkle 1 tsp. salt over the meat.
Turn on the exhaust fan. Heat 2 Tbs. of the oil in a large, heavy flameproof roasting pan over medium-high heat. When the pan is hot, sear the roast until browned lightly on at least the two widest sides. Transfer the meat to a tray or platter and then carefully pour the hot fat out of the pan.
Put the dried cherries with their soaking liquid, the breadcrumbs, mustard, rosemary, sage, 1 tsp. salt, the pepper, and the remaining 2 Tbs. oil in a food processor and pulse to make a coarse, wet paste. Scatter the carrots, celery, and onion in the roasting pan to make a bed for the lamb. Put about a third of the cherry paste onto the bottom of the roast (the wide side closest to the bone). Set the roast bottom side down on the vegetables. Pat the remaining paste evenly on the rest of the lamb. Put the pan in the oven and set a timer for 25 min.
After 25 min., lower the heat to 375°F and roast until the temperature at the thickest part of the meat is 125° to 130°F for medium rare, another 35 to 45 min. (or longer if you prefer medium or well-done lamb). Check the roast periodically to be sure the cherry crust isn't getting too dark; if it is, drape a piece of foil loosely over the lamb. Transfer the meat to a carving board or serving platter. Cover the lamb with a sheet of aluminum foil (not too tight, or the meat will steam) and let rest for 10 min.
Meanwhile, set the roasting pan over two burners on medium high, leaving the carrots, celery, onion and any fallen-off crust in the pan. Add the sweet vermouth and broth. Stir and scrape the bottom of the pan with a wooden spoon and let the liquid simmer until it reduces to about 1 cup of slightly thickened sauce, 8 to 10 min. Season the sauce with salt and pepper to taste. Pour the sauce through a fine sieve into a serving bowl. Stir and gently press on the solids in the sieve to free the sauce, but don't break up the solids or force them through the sieve. Discard the solids.
To serve the lamb, carve 1/2-inch slices, discarding the garlic pieces as you come across them. Some of the flavorful crust will fall off while you carve--just spoon it up and serve it alongside the meat. Arrange the sliced lamb on a large serving platter or individual plates and drizzle with the sauce.