2Combine seasonings in a small bowl and sprinkle over the meat.
3Heat a large heavy skillet over high heat and add 1 tablespoon olive oil. Brown lamb on both sides for 3 minutes each side. Pour off fat from pan, but save any juices to make pan sauce later.
4Transfer lamb to roasting pan and roast, fat side up, in the middle of the oven for 13-15 minutes until the internal temperature is 130-135°F for medium-rare. Remove racks to a warm platter and let rest for 10 minutes while you make the sauce.
5Set the original skillet back on a burner. Add stock and scrape up any browned pieces from the bottom of the pan. Reduce to about 1 tablespoon. Add vinegar and remove pan from heat and whisk in the remaining 3 tablespoons olive oil and mint to form vinaigrette. Cut the racks into individual chops and serve, topped with the sauce atop salad greens.