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.
"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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