In the bowl of a food processor fitted with a steel blade, process the salt, rosemary, and garlic until they're as finely minced as possible. Add the mustard and balsamic vinegar and process for 1 minute. Place the lamb in a roasting or sheet pan with the ribs curving down, and coat the tops with the mustard mixture. Allow to stand for 1 hour at room temperature.
Preheat the oven to 450 degrees F.
Roast the lamb for exactly 20 minutes for rare or 25 minutes for medium-rare. Remove from the oven and cover with aluminum foil. Allow to sit for 15 minutes, then cut into individual ribs and serve.
Note: "Frenching" refers to scraping the meat off the tips of the bones. Ask your butcher to leave 1/8 inch of fat on the meat.
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