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 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°F.
Roast lamb for exactly 20 minutes for rare (or 25 minutes for medium rare). Remove from oven and cover with aluminum foil. Allow to sit for 15 minutes, then cut into individual ribs and serve.
Notes
"Frenching" refers to scraping the meat off the tips of the bones. Ask your butcher to leave ⅛ inch of fat on the meat.
Check lamb with an instant thermometer. Rare will be 125 degrees; medium-rare is 130 degrees.