Season the chops well with salt and pepper. Heat a large, heavy skillet over high heat and add 1 tbsp of the oil. Put in the chops (in batches if necessary, adding more oil as needed) and cook for 3 minutes. Turn and cook 145 degrees F for medium-rare, 160 degrees F for medium or 170 degrees F for well. Remove the chops from the pan and cover loosely with foil to keep warm while you make the vinaigrette. The meat's internal temperature will rise about 5°F or so as the chops rest.

Pour off all the fat from the pan, leaving any meat juices behind. Put in the stock and scrape up any browned bits from the bottom of the pan. Boil until the stock and juices are reduced to about 1 tablespoon. Add the vinegar and take the pan off the heat. Whisk in the remaining 3 tablespoons oil to make a vinaigrette. Taste for salt and pepper.

Place the mint leaves in a small bowl and pour the vinaigrette over them. Steep for 3 minutes.

Spread the optional greens on a platter, arrange the lamb chops on top, and pour the vinaigrette and mint leaves over it all. If you're not using the greens, arrange the chops on a platter and pour the sauce and mint leaves over them. Serve at once.