Kumquats are similar to oranges, although they are much smaller and tarter. Sometimes called pear squash, chayote can be eaten raw or cooked. Be sure to use true yams, not sweet potatoes, in this dish.
To prepare the relish, mix together the kumquats, onion, ginger, lemon juice, vinegar and salt. Let sit for one hour before serving at room temperature.
Steam the yams and carrots together for about 30 minutes, until fork tender. Remove from heat. While still hot, add the butter and mash with a potato masher, adding cayenne and salt. Cover and keep warm.
Heat a grill or broiler.
To prepare the slaw, toss together the chayote, cilantro, lemon juice, oil and salt. Let sit for 10 minutes before serving.
Season the chops with salt and pepper. Grill the lamb to mid-rare or desired temperature, 8–10 minutes for medium rare, turning after 4–5 minutes.
To serve: divide the carrot-yam purée among four plates. Slice each two-bone portion of lamb in half and fan out over purée. Arrange chayote slaw beside the lamb and spoon the kumquat relish over the lamb.