Ask your butcher to prepare the rack of lamb. Alternatively, you can prepare it by removing the parchment and the nerve at the base of the ribs and scraping the skin inside the ribcage. French the ribs 3 cm, keeping the trimmings for another recipe.
Boil the potatoes in salted water for 20 minutes, then drain and let cool slightly. Peel and slice them.
Peel and chop the garlic, and strip the thyme leaves. Preheat the oven to 356°F (180°C). Score the fat on the rack of lamb. Season it and sear fat-side down in a large sauté pan with 6 tablespoons of oil for 2 minutes.
Combine the potatoes, garlic, and thyme in a large baking dish. Generously drizzle with olive oil, mix well, and season.
Place the rack of lamb on top and bake for 18 minutes. Remove from the oven, place the rack on a cutting board, and cut into chops.
Serve the cut rack of lamb with the garlic confit potatoes.