Heat oven to 400° F. Heat a large skillet over medium-high heat.
Season the lamb with ¾ teaspoon salt and ½ teaspoon pepper. In 2 batches, brown the chops, about 2 minutes per side.
Transfer to a baking sheet. Roast to the desired doneness, 4 to 6 minutes for medium-rare.
Meanwhile, in a large bowl, combine the beans, oil, shallots, mint, capers, vinegar, ½ teaspoon salt, and ¼ teaspoon pepper. Serve with the lamb.