With the rack in the middle position, preheat the oven to 180 ° C (350 ° F).
Thoroughly trim the fat off the lamb racks and clean the bones, if needed, or ask the butcher to do it. Season the meat with salt.
In a skillet, brown the meat in the oil and butter. Remove the meat from the pan and set aside in a baking dish.
In the same skillet, add the remaining ingredients and reduce until the sauce is syrupy, about 5 minutes. Put the lamb back in the skillet and coat with the sauce.
Transfer back to the baking dish. Cover with the remaining sauce.
For medium-rare, bake for about 10 minutes or until meat thermometer reads about 60 °C (140 °F). Remove from the oven. Cover with aluminum foil and let rest a few minutes before slicing. Serve with Herb and Cheese Soufflés or the Maple Syrup Mashed Acorn Squash.
As for the rack of lamb, it is important to ask your butcher to saw the bone between the ribs, under the rack, to help with cutting at service.